Whisk flour, 1 tablespoon white sugar, baking powder, and salt together in a bowl. Mix milk, egg, and vanilla extract together in a separate bowl. Stir milk mixture into flour mixture until incorporated.
Beat banana in a bowl with an electric mixer until smooth and creamy; mix creamed banana into batter. Stir melted butter into batter. Refrigerate batter for 10 minutes.
Heat oil in a skillet over medium heat. Drop batter by large spoonfuls into the hot oil, and cook until bubbles form and the edges are dry, 3 to 5 minutes. Flip, and cook until browned on the other side, 3 to 5 minutes. Repeat with remaining batter.
Combine 1 cup white sugar, buttermilk, and butter in a saucepan over medium heat until sugar is dissolved. Bring to a boil for 1 minute; reduce heat and mix coconut extract and baking soda into the syrup. Simmer until baking soda is dissolved, 1 to 2 minutes.