Pesto alla Genovese

Name: Pesto alla Genovese
Ingredients: For the pesto:; 1 or 2 cloves of garlic; a pinch of coarse sea salt; 2 ounces of basil leaves (one large bunch of basil); 1 to 2 tablespoons pine nuts; 2 tablespoons grated pecorino cheese; 6 tablespoons of grated Parmesan; 1/3 cup 1/3 cup (delicately flavored) extra virgin olive oil; For the pesto ricco:; 11 ounces dried pasta such as linguine (see notes above); 2 small-medium sized potatoes, peeled, quartered then cut into ¼ inch slices; 1 cup green beans, cut into 1 inch sections; extra virgin olive oil