For 4-6 servings:
Wash and dry the basil leaves, then put them in a stone mortar with the garlic and the pine-kernels (pressing the basil against the sides with circular movements rather than actually pounding it). Continue grinding the ingredients, then add the grated cheeses and a pinch of salt. As soon as You have a smooth paste, add olive oil drop by drop, stirring with the pestle like a spoon, until you have a thick, creamy sauce. If You prefer, the pesto can also be successfully made in a blender. Peel the dice the potatoes and top and tail the green beans and cut into short lenghts. Set the vegetables to boil in plenty of salted water, and as soon as they are par-boiled, add the trenette. When the pasta is still al dente, drain together with the vegetables, and pour over both the pesto sauce diluted with two dessert-spoons of the cooking water. Mix thouroughly, and serve.