For the pancakes: Combine the banana, flour, 2 teaspoons of the oil, the baking powder, vanilla, cinnamon, salt and egg in a medium bowl and mix until smooth.
Heat the remaining 1/2 teaspoon oil in a large nonstick skillet set over medium heat. Pour out the batter, 1/4 cup at a time, onto the pan, making 4 pancakes. Cook for 1 to 2 minutes per side. The pancakes are ready to be flipped when numerous bubbles appear on the surface. Place two pancakes on two plates.
For the topping: Combine the butter, rum and brown sugar in a medium skillet set over high heat. Stir constantly until the butter melts and the sugar dissolves, about 1 minute. Add the bananas and cook for 1 minute, stirring constantly. Remove from the heat, sprinkle in the vanilla and cinnamon, and baste if the cinnamon clumps. Top the pancakes with the cooked bananas and sauce, and serve.
If the sauce separates after cooling, just reheat under low heat and stir until the sauce bubbles.
Make sure to enjoy these pancakes quickly ¿ they will harden as they cool.
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