In a large pan, cook the ground beef on medium-high heat, seasoning it with salt and pepper. Cook until browned, about 6-8 minutes. Add the chopped onion and cook until it's soft and translucent, about 5 minutes.
Melt butter in the pan and stir in the flour until well combined. Cook for 1-2 minutes, then slowly add the beef broth, milk, and Worcestershire sauce. Stir until the mixture simmers and thickens. Add the corn and green beans, mixing occasionally.
Preheat your oven to 350 degrees Fahrenheit. Lightly grease a 9x13-inch baking dish.
Spread the meat and vegetable mixture evenly in the prepared dish. Layer the frozen tater tots on top, then sprinkle with the shredded cheddar cheese.
Bake uncovered in the preheated oven until the cheese is melted and bubbly, approximately 25 minutes.