Cook the Meat: In a large skillet over medium heat, add the ground beef or lamb. Sauté until the meat is browned, using a wooden spoon to break it apart as it cooks. Drain excess fat if necessary.

Sauté the Vegetables: Add the diced onion and carrots to the skillet. Cook for about 5 minutes, or until the vegetables have softened. Incorporate the minced garlic and sauté for another minute, allowing the aroma to develop.

Build the Filling: Stir in the frozen peas, beef broth, tomato paste, Worcestershire sauce, and dried thyme. Season with salt and pepper to taste. Heat the mixture until it reaches a simmer, letting it thicken gently for approximately 5 to 7 minutes.

Add the Mashed Potatoes: Once the filling has thickened, spoon the mashed potatoes over the meat and vegetable mixture in the skillet. Spread them out evenly with a spatula. For an added burst of flavor, feel free to sprinkle shredded cheddar cheese on top.

Finish Cooking: Reduce the heat to low, cover the skillet, and let it cook for another 5-10 minutes, allowing the cheese to melt and the flavors to meld together. If you want a crispy top, you can place the skillet under the broiler for a few minutes, watching closely to avoid burning.

Plate the Dish: After the cheese has melted and is bubbling, take the skillet off the heat. Serve it hot, adding fresh herbs for garnish if you wish.