Brown the ground beef in a large skillet over medium-high heat.
Add the onion, carrots, celery, and garlic. Cook until the vegetables are softened.
Stir in the tomato paste, beef broth, Worcestershire sauce, thyme, salt, and pepper.
Simmer the mixture for 15-20 minutes, until thickened.
Meanwhile, peel and cut the potatoes into chunks. Boil the potatoes until tender.
Drain the potatoes and mash them with butter and milk.
Spread the beef mixture into a baking dish. Top with the mashed potatoes.
Sprinkle the cheddar cheese over the top.
Bake at 375°F for 25-30 minutes, until the potatoes are golden brown.
