Gently wash the basil in cold water and pat dry with a towel. Crush a glove of garlic in the mortar and add some basil (30 leaves per clove), and then a sprinkle of salt. In a gentle circular motion, use the mortar to tear the basil until it turns into a bright green oily liquid. Repeat this process until all the basil and garlic are added. Add the pine nuts and gently crush them into the mixture. Next, add the cheese. When the cheese is mixed in, slowly drizzle in the olive oil and mix together. At this point, the pesto is ready to use.
Prepare the green beans: cut off the ends, and cut them into 2 or 3 pieces. Peel the potatoes and cut them into bite sized cubes. You will cook the potatoes, pasta and beans in the same pot, and so you must time their addition to the pot according. Bring a large pot of salted water (the same one to be used for the pasta) to a boil. Depending on the type of potato and pasta, you will probably add the potato first, then the pasta after a few minutes, and then the beans near the end. (For this pasta, it’s cooking time was 10 minutes, so it went in first, then the potatoes at 5 minutes, and the beans with 2 minutes left.) Cook the pasta until al dente. Drain well, retaining some of the cooking water. Place the pesto in a large bowl and add a few tablespoons of the cooking water. Add the pasta, potatoes and beans to the bowl and mix together. Serve immediately with a sprinkle of Parmigiano.
Note: If you don’t have a mortar and pestle, you can use a food processor, but use it on pulse mode, so as to avoid turning this into a puree. There should be a fine, leafy consistency.