Step 1

Place potatoes in a medium saucepan and cover with 2 quarts water. Add vinegar and 2 tablespoons salt and bring to a boil over high heat. Cook until potatoes are tender, about 7 minutes. Drain and set aside.

Step 2

Meanwhile, combine egg yolks, mustard, lemon juice, garlic, and 2 teaspoons water in bowl of food processor. Run processor until homogenous, about 5 seconds. Scrape down sides of bowl. With processor running, slowly add canola oil in thin, steady stream, stopping to scrape down sides as necessary. Sauce should thicken and come together. Transfer sauce to a large bowl set in a heavy pot lined with a towel. Whisking constantly, slowly drizzle in olive oil. Season to taste with salt, lemon juice, and black pepper. Set aside.

Step 3

Heat oil in a 12-inch non-stick or cast iron straight-sided sauté pan over medium-high heat to 350°F. Add potatoes in single layer and cook, shaking the pan and flipping the potatoes with a spatula or tongs occasionally until golden brown and crisp, about 5 minutes. Remove from heat. Using slotted spoon or wire-mesh spider, transfer potatoes to bowl lined with paper towels. Season to taste with salt and pepper.

Step 4

Pile potatoes in a large bowl, drizzle with allioli, sprinkle with paprika and scallions, and serve, passing extra alli-oli tableside. Extra alli-oli will keep in the refrigerator for at least 1 week.