Preheat oven to 375° F and lightly butter a 9x13" pan (or an equivalent sized vessel)
In a large skillet over medium heat, add the onions, mushrooms, ground beef, a strong pinch of salt, and a grind or two of black pepper. Cook until the meat is no longer pink.
In a bowl, combine the soups, milk, and Lipton soup mix. Add to the skillet and simmer for ten minutes or so.
Remove the skillet from the heat, add the mixed veggies. Stir to combine.
In the baking dish, layer ½ hamburger mix and ½ of the french onions. Repeat.
Sprinkle with cheese and top with Tater Tots
Bake, uncovered for 15-20 minutes, or until bubbly and the tots are golden brown