In a skillet over medium heat, cook the ground beef with the diced onion and minced garlic until the beef is browned. Drain any excess fat, then transfer the mixture to the slow cooker.
Add the kidney beans, diced tomatoes, chili powder, cumin, salt, black pepper, and beef broth to the slow cooker. Stir everything together until well combined.
Cover and cook on low for 6 to 8 hours, until the chili has thickened and the flavors have blended.
About 30 minutes before the chili is done, preheat the oven to 400 degrees F. In a mixing bowl, stir together the cornmeal, flour, baking powder, egg, milk, and vegetable oil until just combined.
Pour the cornbread batter into a greased 8-inch square pan and bake for 18 to 22 minutes, until the top is lightly golden and a toothpick comes out clean.
Ladle the chili into bowls, top with shredded cheddar cheese, and serve with slices of warm cornbread on the side.