Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.
Heat vegetable oil in a large skillet over medium heat. Add onion; cook and stir until softened, about 5 minutes. Add ground chuck; cook and stir until juices run clear, about 5 minutes. Drain grease. Stir in chili with beans, corn, salsa, Cheddar cheese, water, cumin, chili powder, salt, and black pepper.
Spoon meat mixture into a 2-quart casserole dish, smoothing the top.
Blend cornbread mix, milk, and egg together in a bowl to make cornbread topping. Spread thinly on top of the meat mixture in the casserole dish.
Bake in the preheated oven until topping is golden brown, about 40 minutes. Cool for 10 minutes before serving.