These are the things I generally try and find out to get her in a good emotional state

Her dream job
Her dream city
Her favourite hobby
Her favourite food
Who she thinks is the sexiest female celebrity (yes you read that right)
What accent she think is the sexiest accent

The first four are to get her in a positive emotional state, the last two to get her in a bit of a sexual state. But generally if you want to create a deep connection, I think getting to know someone's dreams and goals in life is getting to know them.