If using whole wings, cut off and discard the wing tips and the middle part of the wing, saving the first section; this is the drumette. Cut around the tip of the smaller end of the drumette to release the skin and meat. With your fingers, pull the meat down toward the larger end, cutting through any tendons with a knife if necessary. The meat should end up in a sack at the end of the bone, with the skin inside and the flesh outside.

In a large bowl, mix the sherry, soy sauce, garlic, ginger, scallions, cilantro, and pepper. Add the drumettes, tossing to coat. Cover and refrigerate for at least 6 hours or overnight.

Line a plate with paper towels. In a deep, heavy pot, pour in enough oil to come about 2-1/2 inches up the sides and heat until it reaches 380 degrees F (a rice noodle will puff into a curlicue within 3 seconds at this temperature; a cube of bread turns golden in 15 seconds). While the oil is heating, drain the marinade from the chicken and discard it. Beat the egg, pour it over the chicken, and toss to coat. Put the water chestnut powder or cornstarch in a deep dish or pie plate. Holding the chicken by the bone, dip the meaty part in the powder so it's well coated. Lightly shake off the excess and place it in the hot oil. Repeat with as many drumettes as will fit without crowding.

Cook the drumettes until they're golden, turning so they brown evenly, about 4 minutes. Remove with a slotted spoon or skimmer and set on the lined plate. Repeat the dipping and frying with another batch of drumettes, adjusting the heat to keep the oil temperature constant. Serve hot with the mustard for dipping.

Make Ahead Tips: You can fry these a couple of hours ahead and reheat them in the oven, although they're best when freshly made.