1 pound spaghetti
1/4 cup extra virgin olive oil , plus more for serving
1 medium shallot , minced (about 3 tablespoons)
1/4 cup heavy cream
2 teaspoons finely grated zest and 1/4 cup juice from 3 lemons
1 ounce finely grated Parmesan cheese (about 1/2 cup), plus more for serving
Ground black pepper
2 tablespoons shredded fresh basil leaves
1. Bring 4 quarts water to boil in large Dutch oven over high heat. Add 1 tablespoon salt and pasta to boiling water; cook, stirring frequently, until al dente. Reserve 1¾ cups cooking water, drain pasta into colander, and set aside.
2. Heat 1 tablespoon oil in now-empty Dutch oven over medium heat until shimmering. Add shallot and 1/2 teaspoon salt; cook until shallot is softened, about 2 minutes. Whisk 1 1/2 cups of reserved pasta cooking water and cream into pot; bring to simmer and cook for 2 minutes. Remove pot from heat, return pasta, and stir until coated. Stir in remaining 3 tablespoons oil, lemon zest, lemon juice, cheese, and 1/2 teaspoon pepper.
3. Cover and let pasta stand 2 minutes, tossing frequently and adjusting consistency with remaining 1/4 cup reserved pasta water if necessary. Stir in basil and season with salt and pepper to taste. Serve, drizzling individual portions with oil and sprinkling with cheese.