Cook the Hash Browns: Heat olive oil in a heavy-bottomed skillet over medium heat. Add the shredded potatoes, salt, and paprika, and sauté until golden brown and crispy, about 8-10 minutes. Adjust the heat as needed and season with black pepper to taste.
Cook the Sausage: In a separate nonstick skillet over medium heat, add a little oil or butter. Cook the sausage links for 5-7 minutes, turning occasionally, until browned and fully cooked. Remove from the skillet and keep warm.
Cook the Eggs: In a nonstick pan over medium heat, melt the butter. Crack the eggs into the pan, being careful not to break the yolks. Cook until the whites are firm and set. Season with salt and black pepper.
Prepare the Avocado: Slice the avocado and drizzle with lime juice. Season lightly with salt and black pepper.
Serve: Plate the eggs, sausage, hash browns, and avocado slices. Pour the orange juice into glasses and enjoy your meal!