Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add diced onion and cook until softened, about 3-4 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet. Cook, breaking it up with a spoon, until browned and cooked through, about 6-8 minutes. Drain excess fat if necessary.
Stir in diced carrots, frozen peas, beef broth, diced tomatoes with their juice, tomato paste, dried thyme, dried oregano, salt, and black pepper. Bring to a simmer and cook for 10 minutes until the mixture thickens slightly.
Transfer the beef mixture into a 9×9-inch baking dish and spread evenly.
In a medium bowl, whisk together cornmeal, flour, sugar, baking powder, and salt.
In a separate small bowl, whisk together milk, egg, and melted butter.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Spoon the cornbread batter evenly over the beef mixture in the baking dish, spreading gently to cover the surface.
Bake in the preheated oven for 35-40 minutes, or until the cornbread topping is golden brown and a toothpick inserted into the cornbread comes out clean.
Remove from oven and let cool for 5 minutes before serving.