Heat the oven to 400°F. Slice about 1/4 inch from the top of the garlic head to expose the cloves, place it on foil, drizzle with 2 tablespoons olive oil, wrap tightly, and roast for 35–45 minutes until soft and golden.

Cool the roasted garlic briefly, then squeeze the softened cloves from their skins and mash them into a paste. Bring a large pot of well-salted water to a boil and cook the spaghetti until al dente according to the package directions.

Reserve at least 1 cup of the pasta water before draining the spaghetti. While the pasta cooks, warm 1/4 to 1/3 cup olive oil in a large skillet over medium-low heat.

Add the roasted garlic paste and red pepper flakes to the skillet. Cook for 1–2 minutes, stirring until fragrant, and do not let the garlic or pepper burn.

Add the drained spaghetti to the skillet and toss vigorously. Pour in reserved pasta water a few tablespoons at a time until the oil becomes lightly emulsified and coats the noodles.

Stir in the parsley and season with the 1/2 teaspoon kosher salt, adding more if needed. Serve immediately with Parmesan, if desired.