If needed, adjust an oven rack to the center of the oven. Preheat the oven to 400°F. Grease a baking sheet.
Arrange the prosciutto in a single layer on the prepared baking sheet and bake until crispy, about 6–8 minutes. Remove from the oven and cool completely, then crumble into small pieces.
In a medium skillet, heat the olive oil over medium-high heat. Add the onion and cook, stirring frequently, until soft, about 5 minutes. Add the garlic and cook until fragrant, about 30 seconds. Add the spinach and nutmeg and cook until the spinach has wilted, about 1–2 minutes. Stir in the heavy cream and bring the mixture to a simmer. Cook, stirring occasionally, until the mixture thickens slightly, about 5 minutes. Remove the pan from heat and stir in the cheese. Season with salt and pepper, to taste.
Poach eggs by filling a small saucepan with 3 inches ofwater. Add 1 tablespoon salt and the lemon juice. Bring the water to a simmer over medium heat. Crack an egg in a small bowl, taking care not to break the yolk. Slowly slide the egg into the water. Using a wooden spoon, carefully stir the water around the egg. Cook for 2–2 1/2 minutes until the white has set and the yolk is still soft. Using a slotted spoon, remove the egg from the water and drain on paper towels. Repeat with the remaining eggs.
To serve, place a tomato slice on each salad plate and season with salt and pepper. Spoon 1/4 of the spinach sauce over the tomato slice. Top with a poached egg and sprinkle with the crumbled prosciutto. Serve warm.
