Soak the pistachios in water for about 2 hours. If short on time, briefly boil them instead. Drain and spread on a clean cloth, rubbing to remove the skins.
In a bowl, combine the peeled pistachios with the pine nuts. Add a few basil leaves, the half clove of garlic, and the grated Parmigiano Reggiano.
Zest half a lemon into the mixture, then season with salt and pepper.
Using an immersion blender, blend the ingredients while gradually adding olive oil and enough hot water to reach a creamy texture.
Cook the pasta in a pot of salted boiling water according to package instructions. Once cooked, drain the pasta and transfer it to a bowl.
Mix in the pistachio pesto, adding a splash of cooking water to help combine. Serve hot, garnished with strips of sun-dried tomatoes and a sprinkle of ground pistachios.