Whisk 1 tablespoon soy sauce, 1 tablespoon Shaoxing wine or dry sherry, 1 teaspoon cornstarch, and ¼ teaspoon white pepper together in large bowl. Add 1 pound ground pork and mash with your hands or silicone spatula to combine. Combine 2 tablespoons oyster sauce, 1 teaspoon toasted sesame oil, and remaining 1 tablespoon soy sauce in second bowl.
Heat 1 tablespoon vegetable oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add pork mixture and cook, breaking pork into small pieces, until no pink remains, 3 to 5 minutes. Transfer pork to large plate.
Heat remaining 2 teaspoons vegetable oil in now-empty skillet over high heat until just smoking. Add 1 pound trimmed and thinly sliced asparagus and cook, stirring frequently, until bright green, about 2 minutes. Stir in 3 minced garlic cloves and 1 tablespoon minced fresh ginger and cook until fragrant, about 1 minute. Stir in pork (and any accumulated juices) and oyster sauce mixture and cook, stirring constantly, until heated through, about 1 minute. Serve.
