Open the sweet potatoes. Using a small sharp knife, cut the roasted sweet potatoes in half lengthwise.
Sear the sweet potatoes. In a medium nonstick pan or skillet, heat about 1 tablespoon olive oil over medium until shimmering. Gently add the sweet potatoes cut side down; the potatoes should sizzle right away. Cook just until the potatoes are warmed through, about 3 minutes.
Finish the sweet potatoes. Transfer to serving plates with the cut side facing up. Cut a pocket into the flesh of each sweet potato by slicing down the middle from top to bottom, leaving the skin intact. This is where you will put the fried eggs. Season with a pinch of salt and pepper.
Fry the eggs. In the same skillet, add a little more olive oil and heat until the oil is shimmering. Crack the eggs and cook until the whites are fully set and the edges are golden, about 3 minutes. Season lightly with salt and pepper.
Finish and serve. Top each sweet potato half with a fried egg. Sprinkle with the feta, za’atar, Urfa biber or Aleppo pepper, and parsley. Serve immediately.