Spaghetti With Tomato and Walnut Pesto

Preheat oven to 350 °F. Toast walnuts on a rimmed baking sheet, tossing once, until slightly darkened, 8 –10 minutes. Let cool. Heat broiler. Toss tomatoes with 2 Tbsp. oil on a rimmed baking sheet; season with salt. Broil, tossing once, until tomatoes are blistered and have released some of their liquid, 5 –7 minutes. Let cool. Pulse anchovies, garlic, lemon zest, red pepper flakes, and 1/2 oz. Parmesan in a food processor until finely ground. Add walnuts and half of tomatoes, then, with motor running, stream in 1/3 cup oil; process just until combined. Season with salt. Transfer pesto to a large bowl and stir in black pepper. Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 1/2 cup pasta cooking liquid. Transfer pasta to bowl with pesto and add a splash of pasta cooking liquid. Toss, adding more cooking liquid as needed, until sauce coats pasta. Add basil and remaining tomatoes. Divide among bowls; top with more Parmesan and black pepper and drizzle with oil.