Heat the oil in a medium-sized skillet over medium heat. Add two of the bananas and the honey to the pan and stir-fry until the bottom of the pan is beginning to brown, about 5 minutes. It's okay if the bananas get mashed into kind of a thick paste.
Stir in the rum extract, then remove from heat.
Divide the remaining, uncooked banana slices evenly between four serving bowls. Add 1/4 of the mashed banana mixture on top of each, then top each with 1/4 cup whipped cream.