With kitchen shears or a sharp knife, cut the crab legs lengthwise in half. Remove the crabmeat from the shells and thickly slice. Divide the lettuce between 4 martini or other decorative glasses.
Mound an equal amount of crabmeat in the centre of each glass. Set a spoon of cocktail sauce alongside the crab; garnish with lemon wedges and parsley and serve.
Note: If available, for added visual appeal, choose king crab legs with a small claw still attached. Snap the claw off and use it as an edible garnish as shown in the photograph. Store bought or homemade cocktail sauce can be used for this dish.