In a saucepan over medium heat, boil the potatoes in salted water until tender,
about 15 minutes. Drain.
Using an electric mixer, purée the potatoes with the butter and the milk until smooth. Adjust the seasoning.
Melt the butter in a saucepan over medium heat. Add the flour and continue cooking, stirring constantly, until the mixture begins to brown, about 3 minutes. Stir in the paprika and dry mustard. Add the broth and bring to a boil while stirring with a whisk. Add the remaining ingredients, reduce the heat and simmer until thickened,
about 10 minutes. Set aside.
Line a cookie sheet with paper towels. Set aside.
Cut the bananas in half lengthwise.
With adult supervision, heat the oil in a large saucepan or deep skillet over medium-high heat. Fry the bananas until golden on both sides. Drain well on paper towels.
Serve in banana split dishes.
Using an ice cream scoop, place 3 scoops of mashed potatoes in each bowl. Drizzle with sauce and place a fried banana half in each bowl. Garnish each serving with a cherry tomato and a dollop of sour cream (“whipped cream”). Sprinkle with peanuts. Serve with BBQ Chicken.