Preheat the oven to 375 degrees and grease a 9 x 13 inch pan.
Place the olive oil in a large nonstick skillet and heat over medium heat. Add the breakfast sausage and cook to brown, stirring frequently (4 to 5 minutes). Add the diced onion and bell pepper and stir. Continue cooking over medium heat until the onions and pepper are tender (3 to 4 minutes).
In a large bowl, whisk the eggs, oat milk, mustard powder, onion powder, salt, and scallions.
Place the shredded hash browns and cooked sausage and pepper in the prepared 9 by 13 inch pan. Pour the egg mixture on top.
Transfer to the oven and bake for 25 to 30 minutes, or until the egg mixture is set. Serve warm.