Put the garlic, rosemary, and olive oil in a small skillet and heat slowly until the oil just begins to simmer. Turn the cloves over in the oil and saute for 10 minutes longer. Remove from the flame and let cool for 15 minutes.

Remove the garlic cloves from the oil (reserve the oil) and mash them to a paste with a knife or mortar and pestle. Take the leaves off the rosemary sprig and finely mince them. In a bowl, combine the garlic paste, minced rosemary, and butter and stir until smooth. Season with salt and pepper.

Cut the baguettes in half lengthwise. Spread the cut sides with the seasoned butter and drizzle with a little of the oil used to bake the garlic. Sprinkle with the Parmesan, close the baguettes back up and wrap each in aluminum foil. Cook over medium heat on the grill or in a bed of slow coals for 10 to 15 minutes. Cut into 2-inch-wide slices and serve immediately.