NASB Luke 24:
45 Then He opened their minds to understand the Scriptures
Personal / Possessive Pronoun - Genitive Masculine 3rd Person Plural
Strong's 846: He, she, it, they, them, same. From the particle au; the reflexive pronoun self, used of the third person, and of the other persons.
Noun - Accusative Masculine Singular
Strong's 3563: Probably from the base of ginosko; the intellect, i.e. Mind; by implication, meaning.
This greek word appears 24 times and only in singular form. Its Greek meaning has less to do with the brain and more to do with the brain's understanding. This is the only place where NASB translated the singular Greek word into the plural English word "minds".
composure (1), comprehension (1), mind (20), minds (1), understanding (1).
OP: The singular seems to convey the idea there was a common "mind" which Jesus opened in order for them to understand the Scriptures.
I wouldn't push it as far. The idea was that their independent brains had a common understanding (mindset).
How should the singular "mind" be understood?
They had a common mindset or understanding of the Scriptures. They were unified in their understanding.