Preheat the oven to 375˚F.
Combine the heavy cream and garlic in a small saucepan and bring to a simmer (keep your eye on it—I can’t tell you how many times my cream has boiled over!). Let simmer, stirring occasionally, 5 minutes.
Heat the olive oil in a 10-12-inch skillet (preferably cast iron) over medium heat. Add the shallots, and cook, stirring occasionally, until light golden, about 2-3 minutes. Add the prosciutto and let cook 30 seconds. Pile in a few handfuls of spinach and let it cook down. Keep adding the spinach until it’s all in the pan (it’ll look like it will never fit, but don’t worry, it will!). Cook until wilted. Drizzle with the lemon juice, and season with salt and pepper. Add the garlic cream and stir to coat. Spread everything into an even layer and let simmer until the cream is slightly thickened, about 2-4 minutes.
Crack the eggs into small bowls or ramekins (this will make it easier to pour them into the skillet without breaking the yolks). Using a spoon, make 4 nests in the spinach. Slide an egg into each nest. Grate fresh Parmesan over top.
Place the pan in the oven and bake 7-10 minutes, just until the egg whites are set but the yolks are still runny. Serve the eggs with bread or toast for mopping everything up.