I'm glad I skimmed past the headers on this. Had I read them, I probably wouldn't have read the story, but I liked this a lot. I love that it was Hermione's idea and that McGonagall waited for consent before obliging her, and that McGonagall did oblige her.

but there's something new in her expression that Hermione thinks, suddenly, she could learn. She wonders why a minute ago she couldn't meet those eyes; now she could look at them --

That's wonderful. There's a hint of something, even though Hermione has no idea what the something is yet.