Begin by washing the new potatoes thoroughly. Cut each potato in half and place them in a large pot, cover with salted water, and bring to a boil. Cook for 20-25 minutes until tender when pierced with a fork. Drain and cool slightly.

While the potatoes are boiling, prepare the pesto. In a food processor, combine fresh basil, pine nuts, nutritional yeast, minced garlic, and salt. Pulse until finely chopped. Gradually drizzle in olive oil while blending until smooth. Taste and adjust seasoning.

After draining the potatoes, cool them quickly under cold water to stop the cooking process. Spread out on a clean kitchen towel to evaporate excess moisture.

In a large mixing bowl, add the cooled potatoes along with the pesto. Incorporate the vegan mayonnaise and lemon zest. Season with freshly cracked black pepper to taste. Carefully fold together until evenly coated.

Transfer the potato salad to a serving dish. Garnish with extra toasted pine nuts and basil leaves. Serve immediately or refrigerate for later enjoyment.