Preheat oven to 375°F. Grease a 9×13-inch baking dish.
Brown the ground beef in a large skillet over medium-high heat. Add the onion halfway through cooking and continue until the beef is cooked and the onion is tender. Drain excess grease.
Add garlic and cook for 30 seconds.
Stir in Worcestershire sauce, garlic powder, onion powder, salt, and black pepper.
Reduce heat to low. Stir in cream of mushroom soup, sour cream, milk, and optional vegetables.
Add 1 cup cheddar and stir until combined.
Spread the beef mixture evenly into the prepared baking dish.
Arrange the frozen tater tots in a single layer over the filling.
Bake uncovered for 35 minutes.
Sprinkle with the remaining cup of cheddar and bake another 8 to 10 minutes, until the cheese is melted and the tots are crisp and golden.
Let rest for 10 minutes before serving.