In a skillet over medium heat, add the pine nuts and toast them for about 3-5 minutes, stirring frequently until they are lightly browned and fragrant. Remove from heat and let the nuts cool completely.

In a food processor, combine the cooled pine nuts, fresh basil leaves, garlic cloves, grated Parmesan cheese, and a pinch of salt. Pulse until coarsely chopped. Gradually drizzle in the olive oil while blending until smooth and creamy. Adjust consistency with pasta water or more oil, if necessary.

Bring a large pot of salted water to a boil. Add the bite-sized pieces of gold potatoes and cook for 6 minutes. Add the green beans and cook for an additional 4 minutes. Drain the vegetables and set them aside.

In the same pot, add the trenette pasta and cook according to package instructions until al dente, about 8-10 minutes. Reserve 1 cup of the pasta cooking water before draining.

Return the drained pasta to the pot. Mix 1/4 cup of reserved pasta water with the pesto, then pour over the pasta. Gently toss in the potatoes and green beans until evenly coated.

Serve the Trenette al Pesto warm. Taste and adjust seasoning with salt and freshly cracked black pepper as needed.