The exercise: Take your main characters (and your side characters too, if you want) and find their opposite selves... for example: You have a female protagonist. Who would she be if she were male instead? And vice versa with a male character. Simple really.
You could be as elaborate as you want. Fill out a character profile sheet for the male version of your female, or just find a male actor who your female character would look like. And vice versa. You could do this all day. It's not only a great way to get to know your characters, it's a distraction from that looming scene you've been trying to write. It might even give you some insight for the scene.
Choose the traits you like from the yin side to add to your character's yang and you've got a deeper character. You can do this with same sex versions too. It's merely an exercise in opposites so you get a well rounded character.
It's a project I am still working on. Here's a small example. Marilyn is inspiration for my female protagonist. She would be Paul Newman if she were male.
Now go have fun with some extra curricular character development! Feel free to share your insights in the comments below!