Preheat oven to 350°F with rack in middle. Mince and mash garlic to a paste with a rounded 1/4 teaspoon salt using a heavy knife. Stir together butter, oil, and garlic paste in a bowl until combined well; stir in parsley. Halve loaf horizontally and divide butter mixture between halves, spreading it evenly. Divide cheese between halves and spread it in an even layer. Put halves, cheese side up, on a large baking sheet. Cover the bread with a large piece of foil, tenting it slightly on the top and tucking it under the bread. Bake 15 minutes. Remove foil and turn oven to broil. Broil bread until golden, 1-3 minutes.