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.
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.
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.
4. Add butter, then pasta and ½ cup pasta cooking liquid to pesto. Using tongs, toss vigorously, adding more pasta cooking liquid…
