Make a Court-Bouillon: Pour 6 quarts cold water into a large stockpot. Add carrots, celery, leek, vinegar, lemon, bay leaves, thyme, salt, and peppercorns. Bring to a boil, and cook 30 minutes. Pour into a fish poacher, and set aside until lukewarm, about 45 minutes.

Set fish poacher on stove over two burners. Lower rack so it rests on vegetables; place salmon on rack (remove tail if needed). Add enough water to cover.

Bring to a simmer over medium-high heat; immediately reduce heat to medium-low. Poach salmon 10 minutes per inch of thickness or until an instant-read thermometer inserted into thickest point registers 130 degrees. Remove poacher from heat; let cool until no longer steaming, about 1 hour. Refrigerate salmon in court-bouillon overnight.

Lift salmon on rack from the court-bouillon, and set over a large pan or sink; let drain 30 minutes. Transfer salmon to a clean work surface. Cut through skin near head, and pull skin off top side of fish. Use the back of a knife to scrape off any brown flesh from surface. Using tweezers, pull out bones along back. Slide salmon onto a serving platter. Salmon can be refrigerated, covered with plastic wrap, up to 4 hours before serving.

To serve, cut cucumber lengthwise into very thin strips using a mandoline or vegetable peeler. Arrange strips diagonally across salmon, spacing 1 inch apart. Garnish with remaining cucumber, cress, and chives. Serve with sauce.