How to Make It
Preheat oven to 450°F. Add potatoes to a large saucepan, and cover with cold water. Bring to a boil over medium-high. Reduce heat to medium-low, and cook until almost tender when pierced with a fork, 12 to 15 minutes. Drain potatoes, and spread on a large baking sheet. Using a flat-bottomed cup, gently press potatoes until they begin to crack, being careful not to fully break apart (it’s okay if some do).
Pour 1/3 cup of the olive oil over potatoes, and sprinkle with 1 teaspoon of the salt and 1/2 teaspoon of the pepper. Toss to evenly coat, and spread in a single layer. Bake in preheated oven until crispy and browned, 25 to 30 minutes, flipping halfway through.
Meanwhile, chop 2 ounces of the cheese into chunks. Add to bowl of a food processor with 1/4 cup of the pine nuts. Pulse until finely chopped, about 5 pulses. Add 3 cups of the basil leaves, and pulse until finely chopped, about 8 pulses. Add lemon juice, and remaining 1 teaspoon salt and 1/4 teaspoon pepper. With processor running, drizzle in remaining 1/3 cup olive oil, and process until smooth and emulsified, about 1 minute.
Transfer potatoes to a serving platter, and dollop with pesto. Shave remaining cheese over potatoes. Garnish with remaining 1/2 cup basil leaves and 1 tablespoon toasted pine nuts. Serve immediately.