Preheat the oven to 450 degrees F and line a baking sheet with foil. Spread the tater tots in a single layer on the baking sheet and cook for 10 minutes. Turn each tater tot over and continue cooking until crispy and brown, about 7 more minutes.
While the tater tots are baking, cook the bacon in a skillet over medium heat until brown and crispy. Drain on paper towels.
Drain grease, wipe out the skillet, crumble the sausage and brown it over medium heat. Drain on paper towels.
Drain grease, wipe out the skillet, and add 1 tablespoon butter. Heat until melted over medium heat. Add the chopped leeks and cook until tender, about 7 to 8 minutes. Reserve.
Remove the tater tots from the oven and lower the temperature to 375 degrees. Cool the tater tots for about 10 minutes. Arrange the tater tots in the prepared baking dish.
Tuck the bacon pieces between the tater tots. Crumble the sausage finely and sprinkle on top. Sprinkle the cooked leeks evenly on top.
Whisk the eggs with the milk, salt and pepper. Pour evenly over the tots.
Sprinkle evenly with the cheddar cheese and the Parmesan cheese.
Cook until eggs are set and top is browned, about 30 minutes. Cool on a wire rack for 10 minutes and serve.