This is linguine with pesto in true, Ligurian style with green beans and potatoes. It smells incredible, and I think you will love it when you make this. It will perfume your whole house with the aroma of the Italian Riviera.
Make the pesto: Heat a skillet and lightly toast the pine nuts until fragrant. Set aside. Blanch the basil (to prevent oxidizing) by bringing a pot of water to a boil and preparing an ice bath. Place the basil in the boiling water for 15 seconds; then immediately remove with a slotted spoon to an ice bath to stop the cooking. When the basil is cool, remove, squeeze out the water, and set aside. In a blender, add the basil, pine nuts, garlic, oil, a pinch of salt, and ¼ cup Parmesan. Mix until combined but still slightly chunky. Remove to a bowl and stir in 1/4 cup Parmesan.
Cook the pasta: Bring a large pot of water with three pinches of salt to a boil. Add the potatoes, cover, and bring back to a boil, 2-3 minutes. Add the linguine to the boiling water and after several minutes, add the green beans. Continue cooking until the pasta’s al dente, about 3 minutes less than what the box advises. Reserve 1 cup of pasta water, drain, and return the pasta, potatoes, and green beans to the pot.
Assemble the dish: Toss the pasta water back into the pasta mixture; then stir in the pesto. Add the remaining 1/4 cup Parmesan and toss, using the heat from the pasta to create a rich and aromatic sauce. Place in a serving bowl, top with more Parmesan, and serve.