Step 1

Preheat oven to 350°. Toast walnuts on a rimmed baking sheet, tossing once, until slightly darkened, 8–10 minutes. Let cool.

Step 2

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.

Step 3

Pulse anchovies, garlic, lemon zest, red pepper flakes, and ½ oz. Parmesan in a food processor until finely ground. Add walnuts and half of tomatoes, then, with motor running, stream in ⅓ cup oil; process just until combined. Season with salt. Transfer pesto to a large bowl and stir in black pepper.

Step 4

Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving ½ cup pasta cooking liquid.

Step 5

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.

Step 6

Divide among bowls; top with more Parmesan and black pepper and drizzle with oil.

Step 7

Do Ahead: Pesto can be made 1 day ahead. Cover and chill.