Though Jesus sometimes appears to use the Midrash PaRDeS methods, Midrash  alone IS eisegesis as demonstrated by the rabbis who practice it and have no standard of truth concerning the results.  If that's all that Jesus did, he was certainly authorized to do so by being the "Ghost writer" of the Old Testament. But this is not the case.
Jesus taught his disciples how to read the OT properly.
The proper genre: The OT is a literal history. It contains historical artifacts such as prophecy, poetry, biography, etc. But it is ALSO a parable  wherein every part participates in the mystery which was hidden from the beginning.  God used the lives of people as the words to write his mystery.
Jesus said that those who would enter the kingdom/teaching must come as children.  The mystery of God is hidden in childish riddle. 
The primary tools which Jesus used were childish word-play such as punning, and notarikon. These tools are used elsewhere in SE Biblical hermeneutics referred to as methods of sensus plenior Jesus also used the methods of PaRDeS which are constrained by his rules of sensus plenior. It would appear that the author of the Gospel of Thomas was familiar with the techniques of prophetic riddle and captured them, perhaps as a study guide to learn the methods of Jesus. The Gospel of Thomas is not a Gnostic work, but a riddle book.
Eliezer ben Yose HaGelili has formalized many of the methods of riddle in his 32 rules.
A comparison of the Gospels reveals the proficiency of the authors in using the methods of interpretation and may indicate a sequence of authoring at 10-15 year intervals as snapshots of doctrine being taught in the Hebrew churches to bring the Greek churches up to date on discovers produced through their continuing studies of scripture as guided by the Holy Spirit.
Mark is the least proficient with most of his correlations being fairly literal. He began the story of Christ with the preaching of John the baptist.
Matthew uses puns and notarikon with his use of 'Yeshua' meaning 'Emmanuel' , and Jesus being called a Nazarene. He writes in an interesting analogy to the Old Testament. The OT is literal history (with the lives of the people being used as the words required for the mystery) , with a hidden picture of what God was doing underneath. Matthew appears to write side by side. In four blocks he records what Jesus said, then what he did. He records that Jesus went up the mountain and taught "Blessed o\are the poor in spirit", then came down the mountain and records that Jesus healed a leper, as an example of blessing one who was poor in spirit. Matthew starts the story of Jesus with Abraham, pushing the parable of history to an earlier time.
Luke is more proficient with the mystery and appears to record the adjustments to the teaching which were taking place in the Hebrew churches, sometimes using Mark's version, sometimes using Matthew's. The teachings are not contradictory, but in some cases Matthew's teaching was a little too 'deep' or hard to grasp by those who were not studying deeply, so the church had reverted to Mark's teaching. Sometimes he adds new material that was discovered through more study during the intervening years. Luke starts the parable of Jesus hidden in history with Adam.
John is the most proficient in his use of the mystery. He uses notarikon and gives the meaning of some of the Hebrew letters. He derives the doctrine of John 1:1-4 from the first three words of Ge 1:1. John starts the story of Jesus with Ge 1:1
There is no further reason to surmise the existence of some Q document. The added content comes from the mystery which was hidden from the beginning as they became more proficient in their studies.
The synoptic problem is solved when the hermeneutic used by Jesus is practiced.
There is no eisegesis. Jesus exegeted the OT using methods which eliminate free-for-all allegory, are reproducible, and verifiable.
God wrote in this genre as an analogy of the way he works in the world. We are like fish swimming in the stream. We do what we do, oblivious to the stream. We cannot see it because we are in it. God is all around us. We cannot see him, because if we could we would see nothing but him. Likewise, birds cannot see the air, but fly where they will. God is behind the scenes quietly nudging us to accomplish his will.
The Bible is a history of the fish swimming and the birds flying. Behind the scenes he wrote a book which speaks of Christ, the cross, and his bride, in great detail. When we see the mystery revealed, and recognize how God has worked in it all, we trust that he is behind the scenes working in our lives to accomplish his will, in the same manner.
This is an important point brought to light by the comments: If Jesus did what he did (by whatever name) and was authorized to do so because he is God, then we might not be able to do it, because we aren't God.
But if Jesus did things which he taught to his disciples, and they wrote in such a way as to teach us, then we can do it.
If there is a standard of truth, it weeds out opinions 'put into' the text by the interpreter. The methods of sensus plenior eliminate the Greek debates, and provide a means for collaborative study. It is difficult to solve a riddle. It is easy to validate it. In this way, even children can participate.
Against eisegesis by Jesus:
Though we don't have anyone in the Bible checking to see if Jesus can show his work in the way he uses scriptures, we do have an example of an apostles doctrine being checked for eisegesis. Paul taught the Gospel as taught by Christ, at least he claims to. When he went to Berea, the people there checked his doctrine against the scriptures which they had; the OT. They validated that Paul had nothing new, but what he taught was contained in the scriptures, though they may not have seen it before. Like the men on the road to Emmaus, they now understood the scriptures the way Paul taught.
The secondhand doctrine of Paul (from Jesus) was validated against the scripture. There was nothing there that they could use to accuse him of invention.
(1)De 28:37 And thou shalt become an astonishment, a proverb, and a byword, among all nations whither the LORD shall lead thee.
(2)Eph 3:9 And to make all [men] see what [is] the fellowship of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ:
(3)Mr 10:15 Verily I say unto you, Whosoever shall not receive the kingdom of God as a little child, he shall not enter therein.
(4)Pr 1:6 To understand a proverb, and the interpretation; the words of the wise, and their dark sayings [riddles]].
 "Midrash most commonly refers to the famous compilation of Midrash Rabbah, a compilation of the rabbis' comments on each of the five volumes of the Torah." https://torah.org/series/midrash/ ... Though here we are referring to the methods used by the rabbis who produced it.
 And as demonstrated in SE in discussions like this: https://judaism.stackexchange.com/questions/81819/did-adam-have-intercourse-with-animals