Preheat the oven to 375˚. In a large skillet over medium heat, heat the oil until shimmering, about 2 minutes. Add the onion and sauté until soft, about 5 minutes. Add the ground beef to the onion and sauté, 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 to a 9-by-13-inch baking dish, smoothing it into an even layer.
In a large bowl, mix together the corn muffin mix with the milk. Spread it thinly over the chili mixture. Bake until golden brown on top, 30 to 40 minutes. Remove from the oven and set aside for 10 minutes to allow the casserole to set. Serve with the cheddar and sour cream.