Preheat the oven to 375°F (190°C).
In a large skillet over medium heat, brown the ground beef (or turkey) until cooked through. Drain any excess fat.
Add the diced onion and garlic to the skillet, cooking until the onion is translucent, about 3-4 minutes.
Stir in the black beans, diced tomatoes, corn, chili powder, cumin, salt, and pepper. Let the mixture simmer for about 5 minutes, then remove from heat.
In a separate bowl, combine the cornmeal, flour, baking powder, and sugar.
In another bowl, whisk together the milk, vegetable oil, and egg.
Pour the wet ingredients into the dry ingredients and mix until just combined.
Spread the meat mixture evenly in a 9x13-inch baking dish.
Pour the cornbread batter over the top, spreading it gently to cover the meat evenly.
Sprinkle the shredded cheese on top of the cornbread batter.
Bake in the preheated oven for 25-30 minutes or until the cornbread is golden brown and cooked through.
Remove from the oven and let it cool for a few minutes before serving.