Preparing the crabs

Prepare the cooking liquid by combining 5 liters of water, the white wine, peppercorns, a little thyme, bay leaf and a few parsley stems.
Bring to a boil and cook the crabs over medium heat for 20 minutes. Remove the crabs from the liquid and cool on a platter.
Remove the meat from the shells, taking care to pick off all bits of shell and cartilage.
Flake the crabmeat and season with lemon juice, olive oil and all the chopped herbs.

Preparing the fennel

Trim the fennel with a paring knife; cut into matignon (small dice).
Sauté gently in olive oil with the star anise and cook covered for 30 minutes. Correct the seasoning.

Finishing

Collect the coral from the crabs; purée in a blender and combine with the mayonnaise, thinned with a little liquid cream. Season with a dash of Tabasco.
 
Slice the celery root into 8 cm (3") disks as thinly as possible. Save the trimmings to make the celery root purée.
 
Cut 20 disks, let them dry for 3 hours and then fry in 130° C (265° F) oil. Remove them when they are white and crispy like a potato chip; drain on paper towels.

Making the celery root purée

Cut 100 g (3 1/2 oz.) celery root into cubes; cook in salted water; drain; season. Purée.
Blend into the crabmeat mixture.
Important: the purée is meant just to flavor the crabmeat. You want to preserve the flaked texture of the crabmeat - adding too much purée will create an undesirably liquid texture.

Presentation

Place a ribbon of the mayonnaise-cream-coral sauce around each plate. P
lace a spoonful of fennel in the center of the plate, topped by a celery disc.
Assemble the dish like a layered "mille-feuille": place another spoonful of fennel on top, then a layer of crab; continue until you have formed three layers. Garnish the top with sprigs of fennel fronds.