Preheat the oven to 400 degrees F and lightly grease an 8 by 8 inch baking dish.

Place the potatoes in a pot and cover with water. Bring to a boil and cook for 15 minutes until fork tender.

While the potatoes cook, heat a large skillet over medium heat. Add the ground beef and cook until browned, breaking it up as it cooks.

Add the onion, carrots, and garlic to the skillet. Cook for 5 minutes until the vegetables soften.

Stir in the tomato paste, beef broth, Worcestershire sauce, salt, and pepper. Simmer for 5 minutes, then mix in the frozen peas and remove from heat.

Drain the potatoes and mash them with the milk and 2 tablespoons of butter until smooth.

Spread the beef mixture evenly in the baking dish. Spoon the mashed potatoes on top and smooth the surface. Dot with the remaining tablespoon of butter.

Bake for 20 minutes until the topping starts to turn golden. Let it rest for 5 minutes before serving.