Grate potato on large hole side of box grater. Place grated potatoes in colander and rinse thoroughly. Transfer potatoes to a clean kitchen towel and wring out as much liquid as possible. Drying potatoes thoroughly are key to crispy hash browns. Trim and thinly slice green onions on an angle, keeping white and green portions separate. Coarsely chop roasted red peppers.

Place sausages on one side of prepared baking sheet. Bake 10 minutes, flip, and add bread to other side of sheet. Bake an additional 5-6 minutes, or until sausages reach a minimum internal temperature of 160 degrees and bread is toasted.

While sausages are cooking, place half the butter in a medium non-stick pan over medium heat. Once melted, add potatoes and white parts of green onions. Using a spatula, press potatoes into an even layer to completely cover pan. Cook, undisturbed, 5 minutes, or until undersides are golden brown. Top potatoes with remaining butter. Once melted, flip potatoes and cook, undisturbed, 5 minutes, or until undersides are brown and potatoes are tender. Transfer to a plate and season with 1/2 tsp. salt and 1/4 tsp. pepper.

Place 1 tsp. olive oil in same pan used for hash browns (no need to wipe pan clean) over medium heat. Add liquid eggs and roasted red peppers. Use a rubber spatula to constantly scrape along bottom of pan until eggs are set and a little wet, about 2-3 minutes. Remove from burner, sprinkle shredded cheddar on top, then fold omelet in half. Season to taste with salt and pepper.

Serve hash browns on a plate. Add sausages along with half the omelet. Finish with a piece of toast and strawberry preserves. Garnish omelet with green parts of green onion.