Heat a large skillet over medium-high heat. Add ground beef and cook, breaking it apart with a spatula, until browned and cooked through, about 8-10 minutes. Stir in diced onion and cook until translucent, about 3 minutes, then add minced garlic and cook for another minute until fragrant.
1 lb ground beef, 1 medium onion, 2 cloves garlic
Add frozen mixed vegetables and tomato paste to the skillet. Stir well to combine and cook for 3-4 minutes until vegetables are heated through. Pour in beef broth and sprinkle dried thyme. Simmer the mixture until slightly thickened, about 5 minutes, until the excess liquid has evaporated.
1 cup frozen mixed vegetables, 2 tbsp tomato paste, 1 tsp dried thyme, 0.5 cup beef broth
While the filling simmers, place peeled and chopped potatoes into a large pot of boiling salted water. Cook until fork-tender, approximately 15 minutes. Drain the potatoes thoroughly.
4 large potatoes
Mash the cooked potatoes with butter and warm milk until smooth and creamy. Season with salt and pepper to taste. Set aside.
4 tbsp butter, 0.25 cup milk
Preheat your oven to 400°F (200°C). Spread the beef filling evenly in a baking dish. Top with the mashed potatoes, smoothing the surface with a spatula. Sprinkle shredded cheese over the mashed potatoes.
4 large potatoes, to taste salt and pepper
Bake in the preheated oven for 20-25 minutes, or until the top is golden brown and bubbling. Remove from oven and let rest for 5 minutes before serving.