In a heavy small 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.
Preheat oven to 325 degrees F. 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 cloves 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 for 8 to 10 minutes until heated through and cheese is melted. Serve warm.