Heat a medium-sized non-stick pan to medium/medium high heat. Add 2 tablespoons olive oil and when oil is heated, add the ground chicken to the pan. Cook for 3-3 1/2 minutes until chicken is cooked through. Remove chicken from the pan and place in a bowl. Set aside until ready to use.
Using the same pan from cooking the chicken (no need to dirty another pan!), add anchovies, garlic, 3/4 cup olive oil, and walnuts and cook over medium heat, stirring often with a rubber spatula, until nuts are deep golden and garlic is just turning golden, about 3-5 minutes. (I cooked mine for 3 1/2mins).
Next, add tomato paste and continue cooking, stirring often, until it turns a shade darker, about 2 minutes. Let cool 5 minutes.
Then using the rubber spatula, scrape the tomato walnut mixture out of the pan including all of the oil and transfer it to the food processor. Add the Fresno chile (or hot pepper flakes), Parmesan, lemon juice, and salt and puree until a thick paste forms, approx 30-45 seconds.
Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally until al dente following package cooking instructions. Drain pasta. No need to rinse. Set aside pasta pot.
While the pasta is cooking, prepare the Starchy Water by combining 1/4 teaspoon each of kosher salt and cornstarch with 1 cup cold water. Heat in a microwave on High for 4 minutes. Set aside.
To assemble, use the rubber spatula again to scrape the tomato walnut mixture (including all of the oil) into the large pasta pot. Then add the butter, pasta and 1/4 cup starchy liquid, and ground chicken to the pot. Using tongs, toss vigorously and add more pasta cooking liquid as needed, until pasta is glossy and well coated with sauce. As the final step, place the lid on the pot and shake the pot rigorously 4-5 times to really coat the pasta with the sauce. Taste and season with more salt if needed.
Finally, transfer the pasta onto individual plates or a large serving platter or bowl. Top with additional walnut pieces, parmesan, and/or hot pepper flakes if desired. Serve immediately, while piping hot!