Combine all dry ingredients including bananas and fold in wet ingredients. Let chill for 5 minutes. Form into hush puppy sized balls and fry in 330-degree fryer for approximately 3 minutes or until beignets float. Check the middle to make sure they are fully cooked and coat in granulated sugar (with a little cinnamon and nutmeg mixed into it.)
Place butter and all types of sugar in a sauce pan and melt over medium heat. Once melted, add the remaining ingredients, excluding the bananas. After the sauce has reduced to a caramel consistency add the bananas. To serve, place 2 scoops of vanilla ice cream in a bowl, pour sauce over the top and place hot beignets in the bowl.