Heat the oven to 400°F and butter a metal 9-by-13-inch baking pan. Keep the tater tots frozen while you prepare the filling.
Brown the sausage in a skillet over medium-high heat for 8 to 10 minutes, breaking it into small pieces and cooking it to 160°F. Drain the rendered fat.
Whisk the eggs, milk, salt and pepper until no separate streaks of egg white remain. Spread the sausage and cheddar in the pan, then pour in the eggs.
Arrange the frozen tots in a single layer across the surface. Bake uncovered for 40 to 45 minutes, until the tops are brown and the egg mixture in the center reaches 160°F.
Rest for 10 minutes before cutting into eight portions; the egg layer should hold together when lifted.