Add basil, nuts, cheeses and garlic to a food processor and process until finely and evenly chopped. Add ½ cup olive oil slowly through feed tube of processor. Run machine until pesto is smooth. Scrape down in between if necessary. Taste and add salt.
Boil water in a large pot to cook pasta. Add 1 tbsp salt and pasta. Stir well and cook until tender.
Before draining the pasta, reserve about ½ cup of the water in a measuring cup.
Put the drained pasta in a big bowl. Add butter and 4 ounces of pesto (about half of the pesto this recipe makes). Mix it so the butter melts and coats the pasta along with the pesto. Pour ¼ cup of the pasta water and stir to make a creamy sauce. Add more water and/or pesto per your taste. Add salt if needed. Serve with shaved parmesan or grated parmesan or pecorino.
If using a food processor without a feed chute, add ¼ cup of olive oil with all other ingredients. Process. Then add remaining olive oil and process until smooth.
*** Remaining pesto can be frozen flat in zip bags
*** 4 servings if eaten as a side dish. 2 or 3 servings if eaten as the main dish.