Preheat the oven to 350°F (180°C). Grease a 9×13-inch baking dish (or use an oven-safe skillet/Dutch oven).
Brown the ground beef in a large skillet over medium-high heat, breaking it apart. Season lightly with salt and pepper. Drain excess grease if needed.
Add the onion and cook 3–4 minutes, until softened.
Add the butter and melt. Add the garlic and cook 30 seconds, just until fragrant.
Reduce heat slightly. Stir in the cream of mushroom soup, green chiles, and Worcestershire sauce. Simmer 2–3 minutes. Taste and adjust salt and pepper.
Remove from heat and stir in the cheddar and pepper jack until melted and combined.
Spread the filling in the baking dish (if not using an oven-safe pan). Arrange frozen tater tots on top in an even layer. Season lightly on top if desired.
Bake uncovered 30–35 minutes, until tots are golden and edges are bubbling.
Rest 10 minutes before serving.