Preheat the oven to 350 degrees F. Grease a 6-quart Dutch oven or lidded cast-iron pot with shortening.
Heat a 10-inch skillet over medium-high heat. Add the ground beef and onions and sprinkle with salt and pepper. Cook until beef is no longer pink and the onions are translucent, about 10 minutes.
Add the frozen green beans to the Dutch oven, followed by the beef and onion mixture. In a small bowl, whisk together the cream of mushroom soup and the milk, and pour this over the beef and onion mixture. Top with the frozen tater tots. Cover with a lid and bake for 45 minutes, or until fully heated through. Remove the lid, raise the oven to 400 degrees F, and cook for 25 minutes more, or until the tater tots are a deep golden brown. Serve hot.