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 1 3/4 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.