BOIL large pot of water over high heat. Season the water with salt. Add the pasta and cook until al dente, 9 to 11 minutes. Drain, reserving 1 cup of the cooking liquid.
HEAT the olive oil over medium heat in a large skillet. Add the guanciale and cook, turning often, until golden brown, 10 to 12 minutes.
ADD the white wine and cook until slightly reduced, 2 minutes. Pour in the reserved 1 cup of cooking liquid and bring to a simmer.
ADD the pasta and the grated cheese and toss to coat. Cook, stirring vigorously, until a thick sauce forms, 2 to 3 minutes more. Season with salt and pepper.
DIVIDE the pasta between plates and garnish with more grated cheese and freshly ground black pepper, then serve.