Spray inside of 9-inch square baking dish with cooking spray.
In a big pan, saute sausage over medium heat until it is browned, breaking it up with a fork, 8-10 minutes; drain off fat.
Add in onion; saute for another 2-3 minutes.
Sprinkle in the flour; stir until the flour is combined and coats the sausage and onion.
Cook for about 2 minutes, stirring constantly.
Slow pour in the milk and stir up the bits from the bottom of the skillet; bring to a boil and add in the Tabasco.
Stir in 1 cup of cheese and continue stirring until cheese melts; cool for 10 minutes.
Add in hash browns, green onions, and eggs, stirring until the mixture is combined.
Pour into prepared dish; sprinkle with remaining cheese.
Preheat oven to 350°; bake for 25-30 minutes, until puffed, golden, and set in the center; let rest for 10 minutes before serving.
Note—after step 9, may cover and refrigerate for up to 2 days or freeze for up to 1 month; when ready to use, defrost in the refrigerator overnight, let casserole come to room temperature for about 30 minutes, then bake as directed.