Preheat oven to 425°F (220°C). Spread tater tots on a baking sheet and bake according to package directions until crispy.
In a large skillet, cook the breakfast sausage over medium heat until browned. Do not drain all the grease.
Add butter to the sausage, stirring until melted. Sprinkle in flour and stir continuously for 2 minutes to cook out the raw flour taste.
Gradually add milk while stirring constantly. Simmer until the gravy thickens. Season with salt and black pepper.
While gravy is simmering, cook eggs to your preference (scrambled, fried, or poached).
To assemble, place a layer of crispy tater tots in a bowl, top with cooked eggs, and pour sausage gravy over everything.
Sprinkle with shredded cheese and add any optional toppings you like. Serve immediately.
Notes
For extra crispy tater tots, bake them for 5 more minutes than the package recommends. If making ahead, store gravy and tater tots separately and reheat before serving.