Fill a large pot with about 4 quarts of water and set it over high heat until it comes to a boil.

While the water heats, cut the scrubbed potatoes into 1/2-inch pieces so they cook in the same time as the pasta.

Trim the green beans and cut them in half so they are easy to toss with the pasta and eat in one bite.

Finely grate the Parmesan until you have 3/4 cup. Finely grate the zest from the lemon, then cut the lemon in half.

When the water reaches a full boil, add the kosher salt to the pot.

Add the fusilli and the cut potatoes to the boiling water. Stir well so the pasta does not stick to the bottom of the pot.

Cook the pasta and potatoes for 6 minutes, stirring once or twice.

Add the green beans to the same pot.

Cook for 4 to 5 minutes more, until the pasta is tender, the potatoes are soft when pierced with a fork, and the green beans are bright green and just tender.

Scoop out 1 1/2 cups of the cooking water into a heatproof measuring cup.

Drain the pasta, potatoes, and green beans in a colander.

Return the empty pot to low heat. Add the pesto and 1/2 cup of the reserved cooking water, then stir until the pesto loosens into a smooth sauce.