Salade Niçoise with Jammy Eggs and Crispy Potatoes

Name: Salade Niçoise with Jammy Eggs and Crispy Potatoes
Ingredients: 6 tablespoons extra-virgin olive oil; ¼ cup lemon juice (2 lemons); 2 tablespoons minced shallot; 2 teaspoons minced fresh thyme; 2 teaspoons Dijon mustard; 4 anchovies , rinsed and minced; ½ teaspoon table salt; ¼ teaspoon pepper; 10 ounces grape tomatoes , halved lengthwise; ½ teaspoon sugar; ¼ teaspoon table salt , plus salt for cooking vegetables; 1½ pounds small red potatoes , 1 to 2 inches in diameter; 12 ounces green beans , trimmed; 6 large eggs; 2 (5- to 7-ounce) jars/cans olive oil–packed tuna , drained and broken into bite-size pieces with fork; ¼ cup niçoise olives; 2 tablespoons capers