Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic, diced carrots, and diced celery to the skillet. Cook for another 5 minutes until vegetables begin to soften.
Add ground beef to the skillet. Cook, breaking it up with a spoon, until browned and cooked through, about 7-8 minutes. Drain excess fat if necessary.
Stir in tomato paste, Worcestershire sauce, dried thyme, dried rosemary, salt, and black pepper. Mix well.
Pour in beef broth and bring to a simmer. Cook for 10 minutes until the mixture thickens slightly. Stir in frozen peas and remove from heat.
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 together milk, vegetable oil, and eggs until combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Spoon the cornbread batter evenly over the beef mixture in the baking dish, spreading gently to cover completely.
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.