For the sausage: Cook in a 400°F oven to an internal temperature of 160°F using a thermometer.
Shred potatoes with box grater.
Heat a non-stick pan over medium heat. Once hot, add the oil, potatoes, paprika, onion powder and garlic powder. Season well with salt and a little pepper. Sauté until the potatoes start to turn golden brown, then lower the heat to medium low, stirring occasionally until they are tender. Season with salt if needed.
Heat a non-stick pan over low-medium heat. Once hot, add a little oil. Saute the onion and pepper until softened. Pour in the eggs and reduce the heat to low. Use a spatula to pull the cooked eggs into the center, letting the liquid egg fill the space behind it. Continue going around the pan, pulling the eggs towards the center until the eggs are nearly set. Once the omelet is sliding around the pan easily and you can get a spatula underneath, flip the omelet over and turn off the heat. Sprinkle cheese over the egg and fold the omelet in half. Repeat for all portions.
Serve the omelet with hash browns, sausage, and toast (buttered if desired).