Place the potatoes in a medium pot, cover with water, and boil until fork tender. Drain, then mash with the milk and butter until smooth. Set aside.
In a large skillet, cook the ground beef over medium heat until browned. Add the onion, carrots, and garlic. Cook for 5 minutes until the vegetables begin to soften.
Stir in the flour and cook for 1 minute. Add the beef broth, Worcestershire sauce, thyme, salt, and pepper. Simmer for 5 minutes until the mixture thickens.
Stir the frozen peas into the beef mixture and remove the skillet from heat.
Transfer the beef and vegetable filling to a baking dish. Spread the mashed potatoes evenly over the top.
Bake at 400 degrees Fahrenheit for 20 minutes until the topping turns lightly golden.