Step 1

Cook anchovies, garlic, oil, and walnuts in a small saucepan over medium heat, stirring often, until nuts are deep golden and garlic is just turning golden, about 5 minutes. Add tomato paste and cook, stirring often, until it turns a shade darker, about 2 minutes. Let cool 5 minutes.

Step 2

Scrape walnut mixture, including the oil, into a food processor and add chiles, Parmesan, lemon juice, and ½ tsp. salt; pulse until a thick paste forms. Scrape pesto into a large bowl.

Step 3

Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain pasta, reserving 1½ cups pasta cooking liquid.

Step 4

Add butter, then pasta and ½ cup pasta cooking liquid to pesto. Using tongs, toss vigorously, adding more pasta cooking liquid as needed, until pasta is glossy and well coated with sauce. Taste and season with more salt if needed.

Step 5

Do Ahead: Pesto can be made 5 days ahead. Cover and chill.