Special equipment: a panini maker
Preheat a panini maker to medium heat.
Spread the peanut butter on one side of each slice of bread. Arrange the banana slices on top of the peanut butter on one of the slices. Top with the other slice of bread to make a sandwich. Butter the outside of the sandwich on both sides.
Put the sandwich in the panini press and close (do not press on the panini maker or the filling will leak out). Cook according to the panini maker instructions until the bread is lightly browned and crispy. Let cool for 3 to 4 minutes, then slice into sticks and serve.