Preheat your oven to 400°F (200°C) and line a large rimmed sheet pan with parchment paper for easy cleanup.
Peel and dice the sweet potato into small 1/2-inch cubes, and chop the bell pepper and red onion into bite-sized pieces.
Place the sweet potatoes, peppers, and onions on the sheet pan, then crumble the ground turkey sausage into small chunks across the tray.
Drizzle with extra virgin olive oil and sprinkle evenly with smoked paprika, garlic powder, sea salt, and black pepper.
Toss everything together with your hands or a spatula until well coated, then spread into a single even layer.
Roast in the center of the oven for 20 minutes, or until the sweet potatoes are tender and the sausage is fully cooked through.
Remove the pan and use a spoon to create two small wells in the hash; carefully crack one egg into each well.
Return the pan to the oven and bake for an additional 5 to 7 minutes until the egg whites are opaque and set, but the yolks remain slightly runny.
Serve immediately, ensuring each portion includes one egg and a generous heap of the sausage and vegetable hash.