Preheat oven to 350 degrees F.
Cut the top quarter from each head of garlic and set on a foil-lined baking sheet. Drizzle 2 teaspoons of the oil over the tops and sprinkle with 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper. Place on the pan, cut side down, and roast until the cloves are tender, but still firm enough to slice, 30 to 35 minutes. Remove from the oven and let sit until cool enough to handle. Squeeze the garlic cloves from the pod, and cut into slivers.
Roast the peppers by placing them on an open gas flame, turning frequently with tongs until all sides are charred black, 7 to 10 minutes. (Alternately, the peppers can be roasted under a broiler, or on top of a gas or charcoal grill.) Place the blackened peppers in a plastic or paper bag, and let rest until cool enough to handle, about 15 minutes.
Preheat the oven to 400 degrees F.
Peel the peppers, make a slit down 1 side, and open flat. Remove the seeds and the stems. Season each pepper with a pinch of salt and pepper. Lay the peppers flat. Place the mozzarella and basil inside and roll together into a spiral. Place in a baking dish and bake for 5 minutes, to heat through.
In a large skillet, heat the remaining 2 tablespoons of oil and the butter and melt the butter over medium heat. Add the roasted garlic and cook, stirring, for 1 minute. Add the white wine and cook for 1 minute. Remove from the heat.
Bring a medium saucepan of salted water to a boil. Add the pasta and cook until al dente, about 7 minutes if dried, or 2 minutes if fresh. Drain in a colander. Add the drained pasta to the white wine mixture with the basil and toss to coat evenly. Season, to taste, with salt and pepper.
Place the pasta in serving bowls. Top the pasta with the peppers and sprinkle with shaved Parmesan.
Yield: 4 servings