Place egg in a small saucepan, and cover with cold water by 1 inch. Bring to a boil. Remove from heat. Cover, and let stand 13 minutes. Using a slotted spoon, remove egg, and rinse under cold water until cool. Gently press against a hard surface to crack shell; peel. Cut egg in half lengthwise. Grate each half on the small holes of a grater into a small bowl. Cover with plastic wrap; set aside.
Preheat oven to 350 degrees. Place salmon in a 13-by-9-inch nonreactive baking dish. Brush with 1 teaspoon oil; season with 1 teaspoon salt and 1/4 teaspoon pepper. Cover with foil; bake until salmon is cooked through and flakes easily, about 15 minutes. Uncover partially, and let cool slightly in dish on a wire rack. Using a fork, gently flake salmon into large pieces. Transfer to a large bowl.
Whisk together lemon juice, hot sauce, and remaining 1/4 teaspoon salt in a bowl. Add remaining 2 teaspoons oil, whisking until emulsified. Drizzle dressing over salmon, and toss gently. Divide among plates. Scatter shallot, capers, cornichons, chives, parsley, and egg over each, dividing evenly; season with pepper. Serve with lemon wedges.