Preheat oven to 375 degrees F.
In a medium skillet over medium heat, heat the extra-virgin olive oil and the butter and sweat the shallots a few minutes. Add the spinach and stir in the cream, season with salt, freshly ground black pepper and a little grated nutmeg. Cook the spinach, stirring occasionally, until the cream has thickened, 5 minutes. Adjust seasoning to your taste.
Fold each slice of ham or prosciutto in half and line the nonstick cups with 1 slice of meat each. Spoon a heaping tablespoon of the cooked spinach into each of the cups, then crack an egg into each, making sure it stays whole (hint - if you're worried about breaking the egg yolk, crack the egg into a small bowl first, then pour it into the muffin cup). Season the tops of the eggs with salt and freshly ground black pepper and bake in the oven until set, about 15 minutes. Allow the baked eggs to cool in the muffin cups for a couple of minutes before removing them from the pan. Serve immediately.