In a large saute pan, heat the oil over moderately-high heat. Add the onion, garlic and red pepper and cook, stirring, until softened and beginning to brown, 3 to 5 minutes. Add the sweet potatoes, turkey, salt and pepper and cook, stirring occasionally, until the potatoes are beginning to brown, about 6 to 8 minutes longer. Add the broth, heavy cream and chives, cook for another 2 to 3 minutes, scraping up any brown bits that may have formed on bottom of pan. Keep warm while frying eggs.

In a large, nonstick saute pan, melt the butter over medium high heat. When the butter is foamy, carefully crack the eggs into the pan and season lightly with salt and pepper. Reduce the heat to medium-low, cover and cook until the whites are firm, 2 to 3 minutes.

Divide the hash equally between 4 warm plates, remove the eggs from the pan, and divide the eggs between the plates. Serve with mesclun greens drizzled with olive oil.