It's on the tip of my tongue. The great thing about this word is that there's a connotation that a person it describes is not just smart or curious, but that they find a childlike joy in learning.
This word is paired with the word "intellectually", as in "intellectually curious." But when it's on its own, it's more likely to be describing someone who's cheeky or sassy, particularly a child. But in that usage, there's the connotation that their cheekiness or sassiness belies gifted intelligence.
I am pretty sure it starts with a p, or even maybe 'pro,' but I could be wrong about that.