2) In a nonstick pan, heat 2 tbsp of the olive oil over high heat until the oil shimmers. Sear the potato cakes until crispy and browned, 3 to 5 minutes per side. Transfer to a baking sheet to keep warm in a low oven.
3) Add the spinach to the pan and cook, season with salt and pepper, and toss until just wilted, 1 to 2 minutes. Transfer to a bowl. In the same pan, add the remaining 2 tbsp of oil and cook the onions, garlic and thyme until soft and slightly brown, 10 minutes. Add the tomatoes and olives and cook until warmed. Transfer to a bowl and cover with foil to keep warm.
4) Melt the butter in the same pan and fry the remaining eggs, sunny-side up, or as desired, about 4 minutes. Season with salt and pepper. While the eggs fry, divide the potato cakes among 4 plates. Top with the wilted spinach. Top each cake with a fried egg, and spoon warm tomato sauce over and around the egg.