Put an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Spray a baking sheet with vegetable oil cooking spray.
Arrange the prosciutto in a single layer on the prepared baking sheet and bake until crispy, about 6 to 8 minutes. Remove from the oven and cool completely before crumbling 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 to 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 the heat and stir in the cheese. Season with salt and pepper, to taste.
Fill a small saucepan with 3 inches of water. 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 to 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.
Cook's Note: The poached eggs can be made ahead of time if stored in water and refrigerated. Reheat by placing in simmering water for 30 seconds.