On a large griddle or skillet over low heat, melt 2 tablespoons of butter. Watch carefully and do not burn.
In a small bowl, combine peanut butter, honey, and cinnamon. Slice the bananas into ¼-inch thick slices. Spread the peanut butter mixture on 4 slices of bread and cover with banana slices. Top with the remaining 4 slices of bread. Spread the remaining butter on both sides of each sandwich. Grill the sandwiches lightly on each side until just golden. Cut in half diagonally and serve hot.
