1Heat the oven to 400°F. Have a 9x13 baking dish ready; no need to grease it.
2Brown the ground beef in a large skillet over medium-high heat, breaking it up, about 7 minutes. Spoon the beef into a bowl, leaving about 1 tbsp of fat in the pan (pour off extra).
3Add the onion and mushrooms to the same skillet with a pinch of salt. Cook until the mushrooms release their liquid and start to brown, about 8 minutes. Stir in the garlic and thyme for 30 seconds.
4Drop in the butter, then sprinkle over the flour and stir for 1 minute until no dry spots remain. Slowly pour in the beef broth, then the milk, stirring constantly. Simmer 3 to 4 minutes until thick enough to coat a spoon.
5Stir in the Worcestershire, the browned beef, and the frozen green beans. Season well with salt and pepper; the tots will soak up some of the seasoning, so be bold.
6Spread the mixture evenly in the baking dish and scatter 1 cup of the cheddar over the top.
7Arrange the tots in tight rows over the cheese, covering the surface completely.
8Bake uncovered for 35 to 40 minutes, until the filling bubbles at the edges and the tots are deep golden. Scatter the remaining cheddar on top for the last 5 minutes.
9Let the dish rest 10 minutes so the gravy sets, then scoop and serve.