Cooking them two ways makes the texture of these potatoes outstanding. Boiling them makes them tender, while sautéing them adds a golden, crisp crunch.
Put the potatoes in a large saucepan and cover by 2 inches with cold water. Add 2 tablespoons of salt to the pot. Bring to a boil over high heat and cook, partially covered, until a knife or skewer inserted into the center of each potato meets with no resistance, about 25 minutes. Drain and transfer to a sheet pan to cool slightly.2.
While the potatoes are cooking prepare the pesto. Prepare an ice bath in a medium bowl.3.
Bring a small pot of water to a boil, add the green onions and cook for 30 seconds. Drain in a colander and immediately transfer to the ice bath. Let sit for 2 minutes, then drain again in colander, then drain on paper towels.4.
Combine the onions, parsley, garlic and pine nuts in a food processor and process until coarsely chopped. Scrape down the side of the bowl. Add the cheese and pulse a few times. With the motor running, add the olive oil and continue processing until smooth. Season with salt and pepper. Transfer to a bowl and cover with plastic wrap pressed directly onto the surface of the sauce until ready to use.5.
When the potatoes are cool enough to handle, slice crosswise into 1/4-inch thick slices. Heat about 1/4 cup of canola oil in a large nonstick or cast iron pan over high heat until the oil shimmers. Add the potatoes, season with salt and pepper, and cook, carefully turning with a metal spatula, until lightly golden brown on both sides, about 8 minutes. Add some of the pesto and fold into the potatoes.