For the crab, prepare a large ice bath. In a large nonreactive pot, bring water, wine and aromatics to a boil and allow to simmer for 15 minutes. Season the court bouillon aggressively with sea salt. Bring to a rolling boil, then carefully slip the crabs into the pot and cover. Once the crabs have turned bright red (11-14 minutes), remove them carefully with tongs and plunge into the ice bath to arrest cooking. Begin to clean crabs as soon as they are chilled. Place a colander in the sink or over a work bowl to use as you discard shells and viscera. Remove the large head shell by firmly grasping the shell with a kitchen towel and pulling away from the body. Reserve the shell for presentation. Remove and discard the gills, then wash the body of all viscera. (If allowed to stay in contact with the meat, it will stain it an unattractive grey.) Break the crab in half, then remove the legs. Carefully crack the legs with a mallet or the back of a kitchen knife. Try to remove the meat in one piece by bisecting the body lengthwise and use a chopstick or wooden skewer to push the meat out of the many cavities. Carefully pick through the meat and reserve. Crab may be prepared up to two days in advance and kept well wrapped in the coolest part of the refrigerator.
For the hazelnut vinaigrette, combine all ingredients except the oils in a non-reactive bowl. Whisk to combine, cover with plastic wrap and allow to rest for 30 minutes. Remove the plastic wrap and slowly incorporate the oils in a fine stream while whisking to emulsify. Season with salt to taste and reserve.
10 minutes prior to serving, toss the cucumber and persimmon with seasoned rice wine vinegar and kosher salt. Allow to marinate for 10 minutes.
To serve, carefully fold the crab, marinated cucumber and persimmon, avocado and ¼ cup hazelnut vinaigrette. Taste for seasoning, then divide among the four reserved head shells. Finish with Sonoma Sand, caviar, cracked hazelnuts and a final drizzle of the vinaigrette.