Preheat oven to 400°F. In a 10-inch oven-proof skillet, cook ground beef over medium-high heat until no longer pink, about 5-7 minutes. Drain off excess grease.
Stir in tomato sauce, tomato paste, ketchup, mustard, hot dogs, chili powder, brown sugar, Worcestershire sauce, cumin, garlic powder, and onion powder. Season with salt and pepper to taste. Reduce heat to low and simmer for about 5 minutes, stirring occasionally, until the mixture thickens slightly.
Smooth filling into an even layer in the skillet. Sprinkle with half of the cheese.
In a separate bowl, stir together the corn muffin mix, milk, egg, and remaining cheese until just combined. Pour over the filling and spread into an even layer, sealing the edges so the chili doesn't bubble through.
Bake for about 22 minutes, or until the cornbread is golden brown and a toothpick inserted in the center of the crust comes out clean.