How to Make It
Separate crayfish heads from tails, reserving 8 whole crawfish for garnish. Remove tail meat and reserve. Reserve tail shells. Separate any attached legs and gills from head. Reserve heads; discard leg portion. Clean shells under running water; drain and transfer crawfish and lobster shells to a rimmed baking sheet. Chill, uncovered, overnight.
Heat oil in a 12-quart stockpot over medium-high. Add lobster and crawfish shells; cook, stirring often, until evenly browned and shells turn dark red, 10 to 12 minutes. Add onions, carrots, celery, leeks, fennel, and garlic; cook, stirring often, until tender, 6 to 8 minutes. Add tomato paste; cook, stirring constantly with a flat wooden spoon, 4 to 5 minutes. Add wine; cook until reduced to 1 cup, 12 to 15 minutes. Add ice, thyme, tarragon, and peppercorns; bring to a simmer over medium. Simmer, uncovered, about 55 minutes.
Simmer stock 30 minutes, skimming off any impurities or fats that rise to the top. Strain mixture through a chinois or fine wire-mesh strainer; discard solids. Wipe stockpot clean. Return stock to pot and cook over medium-low until reduced to 2 quarts, 1 hour to 1 hour and 15 minutes. Strain again and chill until ready to use.