Preheat your oven to 400°F and line a large rimmed sheet pan with parchment paper for easy cleanup.
Place the diced sweet potatoes, bell peppers, and red onions on the sheet pan, then drizzle with the olive oil.
Sprinkle the sea salt, black pepper, garlic powder, and smoked paprika over the vegetables and toss until everything is evenly coated.
Crumble the raw turkey sausage into small pieces and distribute them evenly across the pan, nestling them between the vegetables.
Roast in the center of the oven for 18 to 20 minutes, or until the sweet potatoes are fork-tender and the sausage is browned and cooked through.
Remove the pan and use a spoon to create two small wells in the hash mixture, then carefully crack one egg into each well.
Return the pan to the oven for 5 to 7 minutes, or until the egg whites are fully set but the yolks remain slightly runny.
Serve the hash immediately while hot, ensuring each portion includes one egg and plenty of roasted sausage and vegetables.