Heat olive oil in a large, oven-safe skillet or braiser set over medium-high heat. Add ground beef and cook until no pink remains. Add onion and carrots to the beef and cook until vegetables begin to soften about 4 minutes. Add garlic and cook 1 minute longer. Sprinkle flour, salt, black pepper, and chili powder over the mixture and stir to combine. Stir in the diced tomatoes, tomato paste, Worcestershire sauce, and beef broth. Cook 5 minutes longer, then remove from heat and stir in peas and corn. Preheat the oven to 400°F. Prepare cornbread mix according to package directions or make a cornbread batter from scratch following the recipe in the notes below. Dollop the cornbread batter into drop biscuits over the beef mixture. You should end up with 12-drop biscuits. Do not spread the batter. Bake for 25 to 30 minutes or until the beef mixture is hot and bubbling and a toothpick inserted in the middle of the cornbread comes out clean. During the last 5 minutes of baking, sprinkle the cheese on top of the cornbread. Let the casserole cool for 10 minutes, then serve.