Arrange 12 wonton wrappers on your work surface. Cut the banana into 12 (1/4-inch) slices then place one chocolate square topped with one slice of banana in the center of each wonton wrapper. (See Kelly's Notes.)
Using a pastry brush or your fingers, brush the egg around the edges of the wonton wrappers then place a second wrapper atop the chocolate and banana. Firmly press the edges together so the poppers are sealed.
Line a baking sheet with paper towels. Add at least 3 inches of oil to a large heavy-bottomed stock pot and attach the deep-fry thermometer to the side. Heat the oil until it reaches 360ºF. Carefully add 2 to 3 poppers to the hot oil and fry them for about 2 minutes, flipping as needed, until they’re golden brown. Immediately transfer the poppers to the paper towel-lined baking sheet. Repeat the frying with the remaining poppers, allowing the oil to return to 360ºF between each batch.
Serve the poppers warm alongside caramel sauce for dipping.