Pre-heat the oven to 375°F.
In a medium size skillet over medium heat, heat the EVOO and the butter and sweat the shallots for a few minutes. Add the spinach and stir in the cream and 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 the seasonings, to taste.
Fold each slice of ham or prosciutto in half and line each cup of a nonstick 8-cup muffin tin with one slice of meat. Spoon a heaping tablespoon of the cooked spinach into each of the cups, then crack an egg into each one, 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.