Special equipment: an oyster knife
For the mignonette sauce: Mix together the red wine vinegar, shallots and 1 teaspoon white pepper. Cover with plastic wrap and refrigerate until ready to serve. This sauce can be made 1 day in advance.
For the soy-ginger sauce: Mix together the sesame oil, rice wine vinegar, soy sauce and ginger. Cover with plastic wrap and refrigerate until ready to serve. This sauce can be made 1 day in advance.
Shuck the oysters: Using a thick tea towel, hold an oyster firmly in one hand with the flat side facing up. With your other hand, insert an oyster knife into the oyster's hinge, easing it in where you can; make sure the hand holding the oyster is well protected by the towel. Once you feel the knife firmly anchored in the hinge, twist it to pop open the oyster.
Clean the knife and then slide it along the top shell to release the muscle from the shell; remove and discard the top shell. Run the knife under the oyster to detach it from the bottom shell--this ensures the oyster will slide into your mouth when eaten. Discard any oysters that have an unpleasant odor.
Place the oysters on a large platter filled with crushed iced, and garnish with lemon wedges and parsley. Serve immediately with the sauces on the side.