Add the cubed potatoes to a large pot and cover with water. Bring to a boil and simmer for 10-15 minutes, or until fork tender. Drain and cover with a clean kitchen towel - allow to steam for 10 minutes.
Meanwhile, add all of the pesto ingredients to a food processor and pulse to combine. Taste and adjust seasonings as needed. Set aside.
Combine the potatoes, pesto and red onion in a large bowl. Toss to combine. Serve at room temperature or chill in the fridge. Top with fresh basil right before serving.