In the bowl of a food processor, combine the roasted red bell peppers, cashews, garlic, parsley, Parmesan cheese, salt and pepper. Pulse until combined.
While the food process is running, slowly pour in the olive oil. Process until smooth, scraping down the sides as needed.
Place the potatoes in a large pot of cold, lightly salted water. Bring to a boil, reduce to medium-high and cook until the potatoes are tender when pierced with a fork, 15 to 20 minutes. Take care not to overcook so that the potatoes do not start to fall apart.
Drain the potatoes.
Transfer the pesto to a large skillet and warm the pesto over medium heat.
Add the potatoes and stir to coat.
Transfer to a serving dish, garnish with parsley and serve.