In a large cast-iron or nonstick skillet, heat 1 tsp. oil over medium-high heat. Add bell pepper, then crack 1 egg into the middle of each pepper ring. Season with salt and pepper and cook until egg whites are mostly set but yolks are still runny, 2 to 3 minutes. Gently flip and cook 1 minute more for over easy. Sprinkle with parmesan and place each egg on a slice of toast. Toss salad greens with 1 tsp. oil and season with salt and pepper; serve alongside eggs.
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