Heat oven to 400°F. Cut the top 1/4 inch off the garlic head to expose the cloves. Place on a piece of foil, cut side up. Sprinkle with salt and drizzle with 1 teaspoon olive oil. Wrap tightly in foil and roast until soft and golden brown, 40 to 50 minutes.

Bring a large pot of salted water to a boil. Finely chop the parsley. Cook the pasta according to package directions until al dente. Reserve 1 cup pasta water, then drain.

While the pasta cooks, heat the remaining 1/2 cup olive oil in a large Dutch oven or skillet over medium heat. Squeeze the roasted garlic cloves into the oil and cook, breaking them up with a spoon, until very fragrant, 2 to 3 minutes. Add the red pepper flakes and a few generous grinds of black pepper. Remove from heat.

Return the garlic oil to medium heat. Add the drained pasta, 1/2 cup reserved pasta water, and the parsley. Simmer while tossing constantly, adding more pasta water as needed, until the pasta is glossy and coated.

Serve garnished with additional red pepper flakes, black pepper, and Parmesan if desired.