• Place haddock fillets in a large wide pot.
  • Cover with 5 cups cold water. Place pot over medium-high heat and bring to a simmer. Reduce heat to medium and simmer until fish is just cooked, about 5 minutes.
  • Transfer fish to a plate; let cool. Discard skin and any scales; flake fish into large pieces.
  • Set a strainer over a medium bowl; strain poaching liquid and reserve.
  • [To substitute smoked whitefish for haddock: Discard bones and skin from 1 1/2 pounds smoked whitefish. Put fish, 2 thick-cut slices smoked bacon (about 2 ounces), and 4 cups water in a large wide pot. Bring to a simmer over medium heat; remove fish with a slotted spoon after 5 minutes. Continue simmering liquid (with bacon) until reduced to 2 cups, about 10 minutes. Strain liquid; discard solids. Add 3 cups water; set aside.]
  • Melt butter in a large heavy pot over medium-low heat. Add leek and celery and cook over medium-low heat, stirring often, until soft and translucent, about 15 minutes.
  • Stir in dry mustard, then reserved poaching liquid, potatoes, and thyme sprigs.
  • Increase heat to medium-high and simmer until potatoes are tender, about 12 minutes.
  • With a slotted spoon, remove half of the cooked potatoes and place in a small bowl.
  • Finely mash potatoes with a fork; return to chowder to thicken.
  • Remove chowder from heat and stir in reserved fish, cream, and chives.
  • Serve in warmed bowls with Common Crackers .