Heat oven to 425 degrees. Wrap garlic head in parchment paper-lined foil; drizzle with 2 tablespoons oil, and season with salt and pepper. Roast until soft and golden, about 1 hour. Let cool, trim tip of head; squeeze out cloves, using back of knife. Transfer to small bowl; set aside.
Bring a large pot of water to a boil. Add salt and pasta; cook according to package directions until al dente; drain.
Thinly slice 5 cloves of unroasted garlic; finely chop remaining 3 cloves. Heat remaining 2 tablespoons oil over medium heat in a large skillet. Add sliced garlic; toast until golden and crisp. Using a slotted spoon, remove garlic; set aside. Add chopped garlic; sauté until translucent, about 1 1/2 minutes. Add roasted garlic and white wine; let simmer about 3 minutes. Add pasta, parsley, and red pepper; season with salt and pepper. Toss to combine. Garnish with toasted garlic slivers; serve. Grate cheese over each serving, as desired.
Store extra roasted garlic in a jar filled with olive oil in the refrigerator.