Bring a large pot of salted water to a boil over medium heat. Add the potatoes and cook until just tender, about 12 minutes. Drain well and let cool slightly.
Pulse the basil, mint, garlic, pecans, lemon juice, Parmesan, salt and pepper, to taste, and red pepper flakes in a food processor. Drizzle in the olive oil while the machine is running.
Spoon the pesto into a large serving bowl, then add the potatoes and toss to coat. Serve cold or at room temperature.