Heat half the olive oil in a large skillet over medium heat.
Add the diced potatoes and cook for 8–10 minutes, stirring occasionally, until golden and crisp.
Push the potatoes to the side of the skillet and add the butter.
Sauté the shallot and garlic for 1–2 minutes until fragrant.
Stir in the asparagus and peas, cooking for another 3–4 minutes until just tender.
Add the diced lamb, season with salt, pepper, and nutmeg (if using), and cook for 3–4 minutes, stirring occasionally.
In a separate pan, heat the remaining olive oil over medium heat and fry the eggs to your preferred doneness.
Stir the chopped dill and chives into the hash and remove from heat.
Serve the hash hot, topped with a fried egg on each plate.
Garnish with additional fresh herbs if desired.