Place the eggs in a medium saucepan. Cover with water and bring to a boil. Cover, remove from heat and let stand 15 minutes. Drain and rinse with cold water until cool. Peel and slice in half lengthwise. Remove yolks and set 3 aside for another use, or feed them to your dog.
Meanwhile, heat the oil in a saucepan set over medium heat and sauté the ham for a minute. Add the spinach and cook for another minute, until wilted.
In a medium bowl mash the 3 yolks with the mayonnaise, Parmesan cheese, salt and pepper until smooth. Add the spinach mixture and stir until well blended.
Stuff egg white halves with filling and serve immediately. Makes 12.