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Spray a 9x13-inch baking dish with non-stick cooking spray.
1) In a medium bowl, beat together the eggs and 1/2 milk.
2) In a large non-stick sauté pan, scramble the eggs over low heat until they are just set, about 5-7 minutes. Transfer away from the heat.
3) In a different large sauté pan, over medium heat, cook and crumble the sausage until it is no longer pink, about 7-10 minutes. Transfer the sausage out of the pan to drain on a paper towel.
4) In the same skillet, add the vegetable oil and onions and sauté until softened, about 3-5 minutes.
5) Add the flour and cook over medium heat for 2 minutes.
6) In a medium bowl, whisk in the remaining milk, salt, pepper, nutmeg, and hot sauce.
7) Add the milk mixture to the onions and continue cooking over medium heat.
8) Bring the onion mixture to a simmer and cook until it is heated through, for about 2 minutes. Transfer the onion mixture away from the heat.
9) In a medium bowl, mix together 1 cup mozzarella, 1 cup cheddar cheese, and the parmesan cheese.
10) In the bottom of the prepared baking dish, evenly spread 1/2 cup of the milk mixture, evenly space the lasagna noodles over the milk mixture, pour 1 cup of the milk mixture over the noodles, and evenly spread 1/3 cup each of the sausage, scrambled eggs, and mixed cheeses over the noodles.
11) Repeat the layers twice.
12) Cover the dish with foil and bake for 1 hour.
13) Discard the foil and sprinkle with the remaining mozzarella and cheddar cheeses. Continue baking until the cheese is melted and bubbly, about 15-20 minutes.
Allow the dish to rest for at least 15 minutes before serving.
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