1On a rimmed baking sheet, toast the pistachios for 5-6 minutes. Transfer to a large plate and cool then coarsely grind in a food processor. Transfer the ground pistachios to a bowl and set aside.
2Meanwhile bring a large pot of water to a boil. Add some Kosher salt and the pasta and cook until almost al dente, about 8 minutes. When pasta is almost finished add the broccoli to the pot and cook for 2 minutes more. Reserved 1 cup of the pasta water and drain the pasta and broccoli through a colander.
3In the same processor, combine, garlic, lemon zest and red pepper flakes and kosher salt and grind to a fine paste. Add parsley and mint and pulse to make a rough paste. With the motor running slowly drizzle in the olive oil. Transfer to a medium saucepan and stir in the ground pistachios.
Add the pasta water to the pesto; bring to a boil and simmer for 2 minutes.
In a large bowl, combine the pasta broccoli and pesto. Stir in the lemon h
juice and set aside for 5 minutes. To serve, divided the pasta among plates or bowls and garnish with the grated cheese, chives, sea salt and fennel pollen if using.