Prepare the pesto. Rinse the basil and dry it with a tea towel. Once sliced thinly put the garlic in a food processor, then add the kernels, the walnuts and blast these ingredients; then add the chopped basil leaves and the salt; cover with oil and mix until it is a soft sauce.Add to the sauce the grated parmesan and pecorino, then pour the pesto in a bowl and keep it aside. Trim the French beans, rinse them and chop them into 3 cm size bits.Peel and slice the potato into sticks, keeping them in cold water to prevent them from blackening.In the meanwhile bring to the boil plenty of water, add a pinch of salt and cook the pasta in it. Seven or eight minutes before the pasta is cooked add the French beans and the potato sticks.Pour 2-3 spoonfuls of cooking water of the pasta into the pesto and mix well. Drain the pasta and serve immediately. As tradition has it pesto should be made in the traditional marble mortar, crushing the ingredients against the sides of the mortar itself. The real Genovesi assure an excellent result.