How to Make It
Sprinkle cod evenly with 1 teaspoon kosher salt. Place on a plate; refrigerate, uncovered, at least 1 hour or up to 8 hours or overnight. Combine 8 cups water and kombu in a large pot; cover and let stand at room temperature 1 hour.
Heat kombu mixture over medium-high to about 180°F (water will be steaming, and small bubbles will form around the bottom of the pot, but none should break the surface). Add cod. As the cold fish hits the water, the water’s temperature will drop; adjust heat as needed to maintain water temperature at around 160°F. Cook until a cake tester or a skewer meets no resistance when inserted into fish and fish flakes slighty, 3 to 4 minutes for thin fillets or 8 to 10 minutes for thicker fillets. Using a slotted spoon or a spider, transfer cooked cod pieces to a platter.
Drizzle cooked cod pieces evenly with 1 1/2 tablespoons oil; sprinkle with chives, 1 teaspoon tarragon, 1 teaspoon dill, and flaky salt. Set aside.
Fill a medium pot with water to a depth of 3 inches; bring to a boil over medium-high. Carefully add eggs; cook 6 minutes. Transfer eggs to a bowl filled with ice water; let cool 10 minutes. Peel eggs, and set aside.
Cook shallot and remaining 3 tablespoons oil in a small saucepan over medium-low, stirring often, until shallot is slightly softened but not browned, about 3 minutes. Transfer to a small bowl; let cool 10 minutes. Whisk in capers, lemon juice, Dijon, anchovies, remaining 1 tablespoon tarragon, and remaining 1/8 teaspoon kosher salt.
To serve, drizzle about 1/2 tablespoon tarragon sauce on each of 4 serving plates. Quarter eggs lengthwise; place 3 pieces on each plate. Sprinkle evenly with parsley and remaining 2 teaspoons dill; top evenly with cod, flaking fish as desired. Top evenly with remaining egg pieces. Garnish with parsley and dill, then drizzle and dab the remaining sauce all around. If it looks chaotic, you’ve done it right.