How to Make It
Cook prosciutto in a large skillet over medium, turning once, until crisp, about 3 minutes per side; transfer to a plate.
Add 1 tablespoon of the oil to skillet, then onions and garlic, and cook, stirring often, until golden and soft, 10 to 12 minutes. Add greens and cook, tossing, until wilted, about 2 minutes. Season with ¼ teaspoon each of the salt and pepper; drizzle with lemon juice. Transfer mixture to a bowl and wipe skillet clean.
Preheat broiler with rack 6 inches from heat. Place bread on a baking sheet and drizzle both sides with 2 tablespoons of the oil. Broil until toasted, flipping halfway through, about 1 minute per side. Divide cheese among toasts and broil until melted, about 1 minute.
Place skillet over medium-high heat; add remaining 1 tablespoon oil. Crack eggs into skillet and fry until whites are set and edges are crispy but yolks are still runny, about 3 minutes. Season with remaining ½ teaspoon salt and ¼ teaspoon pepper. Top each toast with some of the greens, prosciutto, and a fried egg.