Not overdoing divrei torah on a date does not mean you are not machshiv torah. A girl does not sit and learn gemara and is most likely not interested in your Rosh Yeshiva’s shiur of the day. I am not saying that a girl wouldn’t appreciate it. I am saying that a date is not the time to share shiurim. End.
A 1st or 2nd date is a time to get to know one another, as yankdownunder said very well.
PS- i had mentioned: a (few?) small dvar/divrei torah is/are ok because it fits in and is enjoyable, without being too heavy. You don’t want to create a very concentrated atmosphere. If you’re discussing something deep that you have in common is another story altogether….