Heat the oven to 400ºF. Meanwhile, cut the tops off 2 heads garlic to expose the cloves. Place each head cut-side up on a sheet of aluminum foil (one sheet for each head). Drizzle each head with 1 tablespoon olive oil. Season the heads with ¼ teaspoon of the kosher salt and ¼ teaspoon of the black pepper. Bring the foil up and around each head of garlic to completely seal. Place on a rimmed baking sheet or small baking dish.

Roast the garlic until the tops are golden brown and very fragrant, about 45 minutes.

Let the garlic sit, still wrapped, until just cool enough to handle, about 15 minutes. Meanwhile, bring a large pot of heavily salted water to a boil over medium-high heat.

Unwrap the garlic. Use the back of a spoon to gently press on the uncut end of the garlic head to squeeze the roasted garlic cloves out. Discard the garlic skin.

Add 1 pound dried spaghetti to the boiling water and cook according to package instructions until al dente. Meanwhile, make the sauce.

Melt 3 tablespoons unsalted butter in a large skillet over medium heat. Add the roasted garlic, remaining ¾ teaspoon kosher salt, and remaining ¼ teaspoon black pepper. Whisk to combine.

Whisk in 1 ½ cups heavy cream, then slowly whisk in 3 ounces finely grated Parmesan cheese and 2 tablespoons lemon juice until combined and bring to a simmer. Continue to simmer, whisking occasionally, until the sauce is thick enough to coat the back of a spoon, about 2 minutes. If the pasta is not ready yet, turn off the heat.

When the pasta is ready, reserve about ½ cup of the pasta water, then drain the pasta. Add the pasta, 1 tablespoon finely grated lemon zest, and ¼ teaspoon red pepper flakes if using to the sauce. Toss over low heat until the pasta is evenly coated in sauce.

Remove the skillet from the heat. Taste and season with more kosher salt and black pepper as needed. Garnish with coarsely chopped fresh parsley leaves and more finely grated lemon zest if desired. If the sauce thickens as it sits, toss in some of the reserved pasta water a few tablespoons at a time to loosen.