Ingredients

• 1 pound small fingerling potatoes
• 1/4 cup kosher salt
• 1 large egg yolk, room temperature
• 1 teaspoon fresh lemon juice
• Coarse sea salt
• 1/2 cup plus 1 1/2 teaspoons extra-virgin olive oil
• 1 tablespoon finely chopped shallot
• 1/2 teaspoon finely chopped fresh tarragon
• Freshly ground black pepper
• 1 1/2 tablespoons drained capers, patted dry
• Vegetable oil or grapeseed oil (for frying)

Instructions

1. Bring potatoes, 1/4 cup kosher salt, and 8 cups water to a boil in a large saucepan and cook until potatoes are tender, about 12 minutes. Drain; let cool completely. Halve potatoes lengthwise. DO AHEAD: Can be made 1 day ahead. Cover and chill.
2. Whisk egg yolk, lemon juice, and a pinch of sea salt in a small bowl. Gradually whisk in 1/2 cup olive oil until mayonnaise forms. Stir in shallot and tarragon. Season to taste with pepper. DO AHEAD: Can be made 4 hours ahead. Cover and chill.
3. Heat remaining 1 1/2 teaspoons olive oil in a small skillet over medium-high heat. Add capers and fry, stirring often, until crisp and golden, 2-3 minutes. Using a slotted spoon, transfer capers to paper towels to drain. DO AHEAD: Can be made 4 hours ahead. Let stand at room temperature.
4. Pour vegetable oil into a large pot to a depth of 2". Attach a deep-fry thermometer to side of pot. Heat oil over medium heat until thermometer registers 375°F. Working in batches, fry potatoes until crisp and dark golden brown, 3-4 minutes. Drain on paper towels. Season lightly with sea salt.
5. Arrange warm potatoes on a platter, cut side up. Spoon some mayonnaise over each; sprinkle with capers.