Preheat the oven to 375°F and lightly grease an 8x8 baking dish.
In a large skillet, cook the ground beef over medium heat until it starts to brown. Add the onion and garlic and cook until the onion softens.
Stir in the carrots and cook for 3 minutes. Add the tomato paste, beef broth, Worcestershire sauce, peas, salt, and pepper. Simmer for 5 minutes until the mixture thickens slightly.
While the filling simmers, boil the potatoes in a large pot of salted water until tender, about 12 minutes. Drain and return them to the pot.
Mash the potatoes with the milk, butter, salt, and pepper until smooth.
Spread the beef mixture evenly in the prepared baking dish. Spoon the mashed potatoes over the top and spread them to the edges. Sprinkle with cheddar cheese.
Bake for 20 minutes until the filling bubbles and the cheese is melted and lightly browned.