Preheat oven to 300°F. Peel and halve the bananas. Heat one T butter in a sauté pan and lightly fry the bananas. Completely combine the egg yolks, 1 C sugar, light brown sugar, and cinnamon. Arrange the bananas in a baking dish and pour the egg mixture over the bananas. Place the egg whites in a clean mixing bowl and whip at high speed until they start to come up. Reduce to medium speed and slowly add the remaining 3/4 C of sugar. Continue beating until stiff. Spread or decoratively bag the meringue over the bananas. Bake for 30 minutes in the preheated oven. Serve warm or at room temperature.