Remove the stems from the mushrooms and finely chop.
Heat 3 tablespoons of the oil in a skillet, add the onion, garlic and chopped mushroom stems and cook gently for 5 minutes.
Add the breadcrumbs and cook until crisp, then stir in the ham, parsley, cheese and salt and pepper.
Arrange the mushroom caps, hollow side up in a greased shallow baking dish.
Fill with the stuffing and sprinkle with a little oil.
Cover loosely with foil.
Bake in a preheated 375°F oven for 25 minutes.
Serve hot, garnished with parsley.