Preheat the oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat.
Add diced onion, carrots, and celery to the skillet and cook for 5 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet and cook until browned, breaking it apart with a spoon, about 7 minutes.
Stir in tomato paste, Worcestershire sauce, dried thyme, dried rosemary, salt, and black pepper.
Pour in beef broth and bring the mixture to a simmer.
Add frozen peas, stir well, and cook for 5 minutes until the sauce thickens slightly.
Transfer the beef mixture to a 9×9-inch (23×23 cm) baking dish and spread evenly.
In a medium bowl, whisk together cornmeal, flour, sugar, baking powder, and salt.
In a separate bowl, whisk milk, egg, and melted butter until combined.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Spread the cornbread batter evenly over the beef mixture in the baking dish.
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 the oven and let rest for 5 minutes before serving.