Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add diced onion and cook until translucent, about 3-4 minutes.
Add minced garlic and cook for another 1 minute until fragrant.
Add ground beef to the skillet and cook, breaking it apart with a spoon, until browned and cooked through, about 6-8 minutes. Drain excess fat if necessary.
Stir in diced carrots and cook for 5 minutes until slightly softened.
Add frozen peas, beef broth, tomato paste, Worcestershire sauce, dried thyme, dried oregano, salt, and black pepper. Stir well to combine.
Bring the mixture to a simmer and cook for 10 minutes until the sauce thickens slightly. Remove from heat.
In a medium bowl, whisk together cornmeal, all-purpose flour, granulated sugar, baking powder, and salt.
In a separate bowl, whisk together milk, melted butter, and eggs.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Transfer the beef mixture into a 9×9-inch (23×23 cm) baking dish and spread evenly.
Spoon the cornbread batter evenly over the beef mixture, smoothing the top with a spatula.
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.