Roast the onion. Heat the skillet over medium heat. Add the red onion half-moons, with a little oil if needed and cook until soft, golden and slightly caramelized at the edges.
Add the tomatoes. Push the onions and tomatoes slightly aside. Lay the tomato rounds in the pan, sprinkle with a pinch of salt and let them warm and soften. Turn the tomato slices over.
Add the eggs and cook low and slow. Crack the eggs into the pan, then sprinkle with salt, black pepper, and parmesan. Reduce to slow-medium heat and cook until the eggs are done to your liking. Cover with a lid for set whites and a soft yolk, or leave uncovered for a runnier egg. Serve warm.