Mix olive oil, garlic, and parsley together in a bowl. Divide mushrooms between two 4-inch round clay dishes that are safe for stovetop use. Ladle olive oil mixture over mushrooms. Cook over medium-high heat, stirring frequently with a small spoon, until oil starts to bubble, 3 to 5 minutes. Remove from heat carefully. Tear up parma ham and scatter over mushrooms. Serve with bread.