Heat 2 tablespoons of olive oil or butter in a large skillet over medium heat. Sauté 1 diced onion for about 3-4 minutes until translucent, then add 2 cloves of minced garlic and cook for an additional minute.

Stir in 2 diced carrots and continue sautéing for 5 minutes, until softened.

Increase heat to medium-high and add 1 pound of ground beef or lamb. Cook until thoroughly browned, about 5-7 minutes, and drain any excess fat.

Stir in 2 tablespoons of tomato paste, 1 tablespoon of Worcestershire sauce, 1 teaspoon each of dried thyme and rosemary, and 1 cup of beef broth. Simmer for 10 minutes until thickened.

Fold in 1 cup of frozen peas and season with salt and pepper, then remove from heat.

While the filling simmers, bring a large pot of salted water to a boil and add 2 pounds of chopped potatoes. Cook for 15-20 minutes until fork-tender.

Drain the potatoes, return them to the pot, and mix in 4 tablespoons of butter and ½ cup of milk, mashing until creamy and smooth.

Preheat your oven to 400°F (200°C). In a 9x13-inch baking dish, spread the meat and vegetable filling evenly across the bottom.

Spoon the creamy mashed potatoes on top and smooth them out. Optionally, sprinkle cheddar cheese over the mashed potatoes.

Bake for 25-30 minutes until the top is golden brown and the filling is bubbling.

Allow the assembled pie to cool for a few minutes before serving.