In a small bowl, lightly beat the egg and vanilla together.
Spread 1 tablespoon of peanut butter on top of each slice of bread. Place the banana slices on top of one of the slices of bread. Place the other slice of bread on top of the first, to make a peanut butter and banana sandwich.
In a skillet or frying pan, melt the butter over medium heat. Dip the sandwich into the egg mixture and place in the heated skillet. Cook until brown on both sides. Serve hot.