Pre-heat the oven to 350 F.
Butter four 3/4-cup (7 ounce) ramekins (about 2 inches wide).
In a large skillet, melt the butter over medium heat.
Adding one handful at a time, cook the spinach until the first handful wilts, then add another handful, until all spinach is wilted and tender. About 4 - 5 minutes.
Drain the spinach in a sieve, pressing to remove excess liquid.
Transfer the spinach to a cutting board, and coarsely chop.
Clean out the skillet with a paper towel.
Add the oil into the skillet over medium heat.
Add the prosciutto and cook until fat starts to render, about 2 minutes.
Add the spinach and the 3/4 cup of cream and bring to a boil.
Cook, stirring often, until the liquid has thickened and reduced by about half, about 6 minutes.
Season with pinches of salt, pepper and nutmeg.
Remove from heat.
Divide evenly among the prepared ramekins.
Gently break an egg onto the top of each ramekin.
Season the top of each with a little more salt and pepper.
Drizzle each with 1 teaspoon of cream.
Gently arrange the ramekins on a rimmed baking sheet.
Bake, keeping a close eye on the eggs to avoid overcooking, until the whites are opaque and the yolks are firm at the edge, but still soft in the center - about 18 minutes.
Remove from the oven.
Sprinkle each serving with 1 teaspoon of the Parmesan cheese.
Serve and enjoy!