In a small heavy saucepan, combine garlic, broth, and wine. Bring to boiling; reduce heat. Boil gently, uncovered, over medium heat about 25 minutes or until garlic is tender and 1/3 cup of the liquid remains. Set aside to cool.
Place rolls (do not separate rolls) in a greased 8x8x2-inch baking pan. Cut an X about 1/2 inch deep into the top of each roll; spread each roll open slightly. Spoon garlic gloves and shredded cheese into the openings in rolls, pressing each down lightly. Drizzle broth mixture over rolls. Brush outsides of rolls with olive oil.
Bake in a preheated 325º oven for 8 to 10 minutes or until heated through and cheese is melted. Serve warm.