How to Make It
Preheat the oven to 350°. Toast the hazelnuts in a small baking pan until fragrant, about 12 minutes. Transfer them to a clean kitchen towel and rub the nuts against each other to remove the skins; let cool completely.
In a food processor, combine the basil, hazelnuts, almonds, walnuts, pistachios, pine nuts, the grated cheese, parsley, garlic and a pinch each of salt and pepper. With the machine on, pour in the oil in a thin stream and process until the nuts are finely chopped. Add the butter and process until blended but still grainy.
Fill a large pot with water, cover and bring to a boil. Add salt and the pasta. Cover partially until the water just returns to a boil, then uncover, stir the pasta and cook until al dente. Drain, reserving 1 cup of the cooking water. Transfer the pasta to a warmed large serving bowl. Add the nut pesto and toss to combine. Add 2 to 3 tablespoons of the reserved past water if the sauce is too thick. Serve immediately.