Preheat your oven to 350°F (175°C). Lightly grease a large baking dish (around 9x13 inches) and set it aside.
In a deep skillet over medium heat, add the ground meat, diced onion, and minced garlic. Cook until the meat is browned, ensuring to break it apart as it cooks. Drain any excess fat if necessary.
In a large bowl, combine the browned meat mixture with potato cubes, sliced carrots, and peas. Pour in the creamy mushroom soup and milk, then sprinkle in the thyme. Stir everything together until well combined.
Transfer the mixture into the prepared baking dish, spreading it out evenly. Cover tightly with aluminum foil, sealing the edges well. Bake in the preheated oven for about 40 minutes.
After 40 minutes, carefully remove the foil and sprinkle the shredded mozzarella cheese over the top. Return the dish uncovered to the oven and bake for an additional 20 minutes, or until the cheese is melted and bubbly.
Once done, take the casserole out of the oven and let it rest for about 10 minutes. This will help the sauce thicken slightly before serving.