Preheat the oven to 375 degrees F.
In a large skillet over medium heat, heat the oil until shimmering, about 2 minutes. Add the onion and saute until soft, about 5 minutes. Add the ground beef to the onion and saute, breaking it up with a spoon, until browned and cooked through, 8 to 10 minutes. Drain off any excess fat. Stir in the salsa, corn, vegetable broth, chili powder, cumin, 1 teaspoon salt and 1/2 teaspoon pepper. Transfer the mixture into a 9-by-13-inch baking dish, smoothing into an even layer.
In a large bowl, mix together the corn muffin mix with about 1 1/2 cups milk, or just enough to make it easy to spread. Spread it thinly over the chili mixture. Bake until browned to top, 30 to 35 minutes. Remove from the oven and set aside for 10 minutes to allow the casserole to set. Top with the Cheddar and sour cream before serving.