Bring 1 inch of water to a rolling boil (24 ounces in the All-Clad pan) in a pan fitted with a steamer basket. Add the eggs, directly from the refrigerator. Cover and steam for 12 ½ minutes.
Transfer immediately to an ice bath; let sit for at least 5 minutes to cool. (See Tip 2)
Remove from the ice bath and dry. Peel.
Slice eggs in half. Remove the yolks to a ricer set over a medium bowl, and rice the eggs into the bowl. (See Tip 3)
Place the egg white halves, curved side down, with the small side facing up. Slice once (short axis orientation). Turn the egg slicer top side down on a cutting board. Make 3 to 4 cross-cuts with a knife for uniform pieces.
Add the mayonnaise, mustard, lemon juice, salt, and pepper to the riced egg yolks; Stir until thoroughly combined and creamy.
Add the chopped egg whites, celery, onions, and dill. Stir gently to combine. Do not overmix.
Cover and chill for 30 to 60 minutes before serving.
Yield: 2 ½ cups.