Lemon Spaghetti with Feta and Basil

Bring an 8-quart stock pot of water to a boil and generously season with salt. Cook pasta according to package directions, until al dente. Drain, reserving 1 cup pasta water. Return pot to stove over medium-high heat. Add olive oil to pot and place lemons cut side down on the bottom of the pot. Sear lemons until they have a golden brown color, about 3 minutes, then remove and set aside. Add butter, garlic, and red pepper flakes to pot; cook until garlic has softened, about 2 to 3 minutes. Add 1 tablespoon lemon zest, juice of 2 lemons, 1 teaspoon salt, 1/2 teaspoon black pepper, and vegetable stock and stir. Add pasta to pot with garlic-lemon mixture. Mix in half the parmesan and feta. (If pasta seems dry, slowly add reserved pasta water until desired consistency.) Just before serving, mix in half the chopped basil. Transfer pasta to a platter and top with remaining parmesan, feta, and basil. Serve immediately.