Make the pesto. Pound the garlic and pine nuts in a large mortar with a little salt. Add the chopped basil leaves (the amount takes into account that basil found elsewhere is less perfumed than in Liguria), a few at a time, pounding and grinding the leaves against the sides of the bowl. Stir in the grated cheese and mix very well, then gradually beat in the olive oil (the olive oil of Liguria is very light, delicate and perfumed) and the prescinsoa or fromage frais, if using. 

Put the potatoes and green beans in a large saucepan with plenty of boiling salted water and cook for 10–15 minutes, then throw in the trofie and cook until these are al dente. Drain, reserving a ladle of the cooking water. Mix with the pesto, diluted if you like with a little of the cooking water and serve with grated pecorino or parmesan.