In a large skillet, over medium heat, melt 2 tablespoon of butter. Add onions, cook until translucent. Add hash browns, season with salt and pepper to taste. Cover and cook until the bottom begins to brown, flip over and cook the other side; set aside.
In another skillet, melt 1 tablespoon butter, cook eggs with a rubber spatula, gently pushing the eggs to the center, until cooked through; cover and set aside.
SAUSAGE GRAVY: Crumble and cook sausage in large skillet over medium heat until browned. Stir in flour until completely combined with sausage. Gradually add warm milk. Cook gravy until thick and bubbly, adding more milk as necessary to control the thickness, season with salt and pepper.
To assemble, spoon hash browns down the center of a tortilla, followed by eggs, gravy and shredded cheese. Wrap folding in both ends and rolling up tightly if you're on the go OR fold one end in and wrap tightly, spooning more gravy over the top