Preparation

1. Peel and cut the potatoes into even-sized chunks. Begin cooking them in cold salted water.
2. In a large skillet, brown the ground beef over medium heat, allowing it to get a nice color.
3. Add diced onion and carrots, cooking until softened.
4. Stir in minced garlic and tomato paste, cooking for 1 minute to deepen the flavor.
5. Pour in beef broth and add Worcestershire sauce, salt, pepper, and thyme, stirring to combine. Allow to simmer until it thickens.
6. Once the potatoes are fork-tender, drain them and let them sit for a minute to release steam.

Making the Mashed Potatoes

1. Mash the drained potatoes with butter first, then gradually stir in warm milk.
2. Add in grated Parmesan and season with salt and pepper.
3. If desired, mix in a beaten egg yolk for extra richness.

Assembling and Baking

1. Let the beef filling cool slightly to prevent the mashed potatoes from sinking.
2. Spread the beef filling evenly in a greased 9×13 baking dish.
3. Dollop the mashed potatoes on top, then spread gently with a spoon, creating peaks with a fork.
4. Bake at 400°F for 20 to 25 minutes, until bubbly and golden. For extra browning, broil for 1 to 3 minutes at the end.