Pack the fennel into a large jar. Add the vinegar, water, sugar, salt, and peppercorns. Give it a good shake. Pickle for 3 hours.
Place the mayo, egg, lemon juice, mustard, Worcestershire sauce, and Old Bay in a bowl. Whisk to combine. Add the crab, crackers, and parsley. Stir to combine. Chill for 30 minutes.
Drizzle the crab cakes with the butter and transfer them to the oven. Bake for 15 minutes.
Turn on the broiler. Place a slice of Jarlsberg on each crab cake and return them to the oven. Broil until the cheese melts
Spread the Old Bay mayo on the slices of rye. Top the bottom slices with a pile of the pickled fennel. Add the crab cake and top with a few leaves of green lettuce and a couple of wedges of avocado.