Preheat oven to 375°F. Grease a 9x13-inch baking dish.
Warm a large skillet over medium-high heat. Add oil if needed, then brown the beef.
Drain excess fat. Stir in onion and mushrooms; cook until softened, about 4–5 minutes.
Add garlic and cook until fragrant, about 30 seconds.
Whisk in soup, milk, Worcestershire, salt, pepper, and paprika. Simmer 2 minutes to thicken slightly.
Fold in green beans and half the cheddar. Remove from heat.
Spread the mixture evenly in the prepared dish.
Arrange tater tots in a snug, even layer on top.
Bake until bubbling and the tots are golden and crisp, 35–40 minutes.
Scatter remaining cheddar over the tots. Bake 5 minutes to melt.
Rest 5 minutes. Finish with parsley and serve warm.