If your shrimp still has the shell on, peel and devein the shrimp. Slice the shrimp in half and transfer the pieces of shrimp to a bowl.
Add the ginger, garlic, scallions, white pepper, salt, oyster sauce, and sesame oil to the bowl. Mix these ingredients with the shrimp until combined.
Lay a wonton wrapper on your work surface. Place one piece of shrimp right above the bottom edge of the wrapper. Roll up the piece of shrimp tightly, like a sushi roll.
To seal the wonton, twist and pinch together the excess wrapper on both ends (to the left and right sides of the shrimp). I usually make two 180º twists on each end and then pinch the twisted portion to make sure the shrimp is adequately sealed inside. Transfer the wrapped wonton to a large plate or sheet pan.
Continue to wrap remaining shrimp filling into the wonton wrappers. If you are working by yourself, you may want to cover the wrapped wontons with a towel to keep the wontons from drying out. (See note 1)
Place a cooling rack on top of a large baking sheet, like a half-sheet pan. You’ll place the fried shrimp wontons on this rack. If you want to absorb some of the oil from frying, line the rack with paper towels. (See note 2)
Pour the oil inside a wok so that you have about 3/4 to 1 inch of oil inside the wok. (See note 3 if you don’t have a wok) Heat the oil over medium-high heat, until the oil reaches about 305ºF to 315ºF (150ºC to 157ºC) degrees. (See note 4 if you don’t have a thermometer to test the oil).
Reduce the heat to medium. Working in batches, carefully add 5 to 7 pieces of shrimp wonton to the wok (however many you can fit without overcrowding). Once the underside of the wontons turn lightly golden, use tongs to flip the wontons over for even browning. I usually fry the wontons for 1 to 2 minutes.
Remove the fried wontons and transfer them to the cooling rack. Continue frying the remaining wontons in batches. If at any point, you notice that the ends of the wontons are turning deep brown within seconds of adding them to the hot oil, the oil is too hot. Reduce the heat to medium-low.
Enjoy the wontons on their own or serve them with my sweet chili sauce. The wontons taste the best when they’re still fresh. (See note 5 below for reheating directions.)