Heat the olive oil in a large (9- or 10-inch) oven-proof skillet over medium-high heat. Add the onions and cook until tender and translucent, about 5 minutes. Add the garlic and cook for another 30 seconds. Add the ground beef and cook, breaking up the beef with a spoon or spatula, and cook until no longer pink, about 5 minutes. Add the tomato paste and cook, stirring, for 1 minute. Add the diced tomatoes, chili powder, cumin, salt, pepper, oregano, pepper, beef broth, and kidney beans. Reduce heat and simmer for 15 minutes.

Preheat the oven to 375 degrees.

In a medium mixing bowl, combine the cornbread mix, milk, vegetable oil, and eggs. Mix well. Smooth over the top of the chili and bake for 30 minutes or until golden brown.