Pat the salmon pieces dry and season with a pinch of salt and pepper. Set aside.
In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the diced sweet potatoes and a pinch of salt. Cook, stirring occasionally, until they begin to brown and become tender, about 8–10 minutes.
Push the potatoes to one side of the skillet and add the onion. Sauté until translucent, 3–4 minutes. Add the garlic and cook for another 30 seconds until fragrant.
Stir in the paprika and cumin. Toss the potatoes and onions to coat evenly with the spices.
Create a space in the center of the pan and add another teaspoon of olive oil or butter. Add the salmon pieces in a single layer and sear for 1–2 minutes per side, just until they start to turn opaque. They don’t need to be fully cooked at this stage—the carryover heat will finish them.
Gently fold the salmon into the potato mixture and cook for an additional 2–3 minutes, until the salmon is cooked through and flakes easily. If you prefer, you can crumble the salmon slightly as you stir to distribute evenly.
While the hash finishes, heat a separate small skillet over medium heat and fry the eggs to your liking, ideally with the yolk still runny for a creamy contrast.
Finish with lemon juice, chopped parsley, and optional lemon zest. Taste and adjust salt and pepper as needed.
Serve the salmon and sweet potato hash hot, topped with fried eggs. A light drizzle of lemon juice over the eggs adds a refreshing brightness.