Combine shrimp, sugar, and salt in medium bowl. Let stand at room temperature for 30 minutes.
Whisk ⅓ cup sherry, soy sauce, chili paste, and vinegar together in bowl. Whisk cornstarch and remaining 2 tablespoons sherry together in second bowl.
Heat oil and garlic in 12-inch nonstick skillet over medium heat until garlic is just beginning to brown at edges, 3 to 4 minutes. Increase heat to high, add scallion whites and ginger, and cook until fragrant, about 1 minute. Add asparagus and scallion greens, cover, and cook, stirring occasionally, until asparagus is crisp-tender, 2 to 4 minutes. Transfer vegetable mixture to bowl.
Add sherry–soy sauce mixture and shrimp to skillet and bring to simmer. Reduce heat to medium-low, cover, and cook, stirring occasionally, until shrimp are just cooked through, 3 to 5 minutes.
Whisk sherry-cornstarch mixture to recombine and add to skillet; increase heat to high and cook, stirring constantly, until sauce is thickened, 1 to 2 minutes. Return vegetable mixture to skillet and toss to combine. Transfer to serving dish and serve.
