Preheat oven to 400 degrees F and line a rimmed baking sheet with a silicone baking mat.
Pre-bake pizza crust according to directions on the package. Set aside when done. Keep the oven on, as you'll be needing to cook the pizza again.
Heat a large non-stick pan over medium heat, then add in sausage, onion, peppers, garlic, salt and pepper.
Cook, breaking up the meat as you go, until the meat is no longer pink and the veggies are tender.
Taste and re-season, if necessary, then remove from the pan and set aside in a bowl.
To the same pan, add in and melt butter.
Once melted, slowly sprinkle and whisk in flour. Cook for 2 minutes, whisking constantly.
Slowly whisk in the milk. Cook, stirring constantly with a rubber spatula until the mixture is the consistency of thick pudding. See video for visuals.
Stir in the whisked eggs and cook until they are soft, but not runny. See video for visuals.
Season with salt and pepper, to taste.
Spread the egg mixture evenly over the pre-baked dough, sprinkle on the cooked sausage/veggies, then top the pizza with shredded cheese.
Bake in the preheated oven and cook for about 15 minutes, or until cheese has melted and the crust has finished cooking.
Sprinkle cooked pizza with sliced green onions.
Slice, serve with optional hot sauce, and enjoy!