In a medium oven proof saute pan, melt the butter and saute the mushrooms and ham for 3 - 5 minutes. Blend the eggs and cream together in a large bowl. Add nutmeg, then salt and pepper to taste. Pour the eggs over the mushroom and ham mixture. Gently stir in the parsley and shredded cheese. Bake in a 375 degree (F) oven for about 20 - 25 minutes or until firm. Serve.