Brown the ground beef in a large pot over medium heat, breaking it up as it cooks. Add the diced onion and minced garlic, then cook until the onion softens.
Stir in the chili powder and cumin. Cook for one minute to toast the spices. Add the black beans, diced tomatoes, and beef broth. Bring the mixture to a simmer and cook for 20 minutes, stirring now and then.
While the chili simmers, heat the oven to 400°F. In a mixing bowl, combine the cornmeal, flour, baking powder, and salt. Whisk in the milk, egg, and melted butter until a batter forms.
Pour the batter into a greased 8-inch square pan. Bake for 15 to 18 minutes until the top turns golden. Let the cornbread cool slightly, then cut it into strips for dipping.