Bring a large pot of salted water to a boil. Add potatoes and cook, uncovered, for 5 minutes. Add green beans and cook, uncovered, for 3 minutes. Use a slotted spoon to remove green beans from water and place in a medium bowl.
Add pasta to pot with potatoes and cook until al dente according to package directions. Drain, reserving ½ cup cooking liquid.
Add pesto and prepared green beans to pasta and potatoes and toss to coat. Add some of the reserved cooking liquid if pasta seems dry. Season with salt and pepper to taste. Drizzle with olive oil and top with additional Parmigiano-Reggiano cheese.
Recipe by Two of a Kind at https://www.twoofakindcooks.com/pasta-green-beans-and-potatoes-with-pesto/