Step 1Bring to a boil a medium-size saucepan full of water. Meanwhile, rinse the basil leaves. Fill a bowl with ice water and place it next to the saucepan, with a skimmer or strainer close by. When the water comes to a boil, salt generously and add the basil leaves. Blanch the leaves quickly to bring out the color, then remove immediately with the skimmer and transfer to the ice water. Drain and squeeze out any excess water.
Step 2In a food processor, pulse the pine nuts until finely ground. Add the blanched basil and ¼ to ½ teaspoon salt, or to taste, and process until finely chopped. With the machine running, slowly add the olive oil and continue to process until the mixture is reduced to a fine puree, about 1 minute. Transfer to a bowl.
Step 3Puree the garlic in a mortar and pestle, or put through a garlic press, and stir into the pesto. Stir in the cheese. You should have about 2/3 cup pesto, which will keep, covered and refrigerated, up to 1 week.
Step 1Place the potatoes in a saucepan and cover with salted water. Bring to a boil, reduce heat, cover partially and boil gently until tender, 10 to 15 minutes, depending on the thickness. Drain, return to the pot, cover and set aside for 5 minutes to steam the potatoes. Cut into ¾ inch-thick pieces and set aside.
Step 2Bring a large pot of water to a boil and salt generously. Meanwhile, fill a bowl with cold water. Add the green beans and boil just until tender, about 4 minutes. Strain into the bowl of cold water to stop the cooking, then drain and set the beans aside.
Step 3Place the pesto in a large, wide serving bowl. Bring the water back to a boil, and add the pasta. Cook to al dente, following the directions on the package. Add 2 tablespoons of the pasta cooking water to the pesto and stir. Remove another 2 tablespoons water in case you want to thin out the sauce a little more when you toss the pasta. Strain the pasta, then add the green beans and potatoes to the pot to heat through. Drain, toss with the pasta and serve.