Preheat your oven to 400°F (200°C) and line a large rimmed sheet pan with parchment paper for easy cleanup.
Crumble the ground turkey sausage into small bite-sized pieces and distribute them evenly across the prepared sheet pan.
Add the diced red bell pepper and yellow onion to the pan with the sausage.
Drizzle the olive oil over the sausage and vegetables, then sprinkle with sea salt, black pepper, smoked paprika, and garlic powder.
Toss all the ingredients together with your hands or a spatula until everything is well-coated in the oil and spices.
Spread the mixture into a single layer and roast in the oven for 15 to 18 minutes, or until the sausage is browned and the vegetables are tender.
Remove the pan from the oven and use a large spoon to create three small wells within the sausage and vegetable mixture.
Carefully crack one egg into each of the three wells, being careful not to break the yolks.
Return the sheet pan to the oven and bake for an additional 5 to 8 minutes, depending on how you prefer your eggs cooked.
Remove from the oven once the egg whites are fully set and opaque, then serve the hash immediately while hot.