Butter the bread slices on 1 side with butter and place them butter side down. Spread 4 slices with peanut butter and top with the banana slices. Spread the remaining slices with jelly and put them, jelly side down, on top of the bananas. Press them gently to flatten them slightly.
Place each sandwich on a preheated panini press and grill until the bread is toasted, about 5 minutes. Alternately, preheat a dry cast iron or non stick pan. Place the sandwich in the pan and weight it down with another pan or a clean brick wrapped in foil. Grill 5 minutes, turn the sandwich over, re-weight it, and grill for another 5 minutes. Serve immediately.