Bring a large pot of water to a boil.

Add potatoes and cook until fork-tender.

Remove potatoes from water and reserve the water.

Cool the potatoes slightly.

Prepare green beans by trimming and french-cutting them.

Blanch green beans until tender.

Remove green beans and set aside, reserving the water.

Peel and slice potatoes into thin rounds or chunks.

Add more water to the reserved stock pot water and bring to a boil.

Prepare pesto by combining basil, garlic, cheese, pine nuts, and salt in a food processor.

Grind mixture to a fine grind, drizzling in olive oil until smooth and creamy.

Taste and adjust seasoning with salt or olive oil.

Set pesto aside.

Cook pasta until al dente in the boiling water with salt.

Reserve some pasta cooking liquid.

Combine cooked pasta, green beans, and potatoes in a large bowl.

Add pesto sauce and mix well.

Thin sauce with pasta cooking liquid as needed to coat ingredients.

Serve immediately with extra grated cheese, if desired.