Preheat grill to medium heat. Slice banana lengthwise with peel on and grill cut side down for 3-5 minutes. Peel bananas and set aside.
Grill tortilla on each side until cooked but still soft, about 1-2 minutes on each side.
While the tortilla is still warm, spread with peanut butter and jelly and then add peeled banana. Roll tortilla into burrito, and using a pastry brush, spread butter on the outside of the tortilla and sprinkle with cinnamon and sugar.
Place the burrito seam side down and grill for a couple minutes on both sides.