Place the potatoes in a pot and cover with water. Boil until fork tender, then drain.
Mash the potatoes with the butter, milk, salt, and pepper until smooth. Set aside.
In a large skillet, cook the ground beef over medium heat until browned. Drain excess fat if needed.
Add the onion, carrots, and garlic to the skillet. Cook for 5 minutes until the vegetables soften.
Stir in the tomato paste, beef broth, and frozen peas. Simmer for 8 minutes until the mixture thickens slightly.
Spread the beef and vegetable mixture evenly in a baking dish.
Spoon the mashed potatoes over the top and spread to cover the filling completely.
Bake at 400 degrees F for 20 minutes until the potato topping turns lightly golden.