Heat a wok over high heat; add 1 tablespoon cooking oil, swirling to coat.
Add the garlic and ginger; cook, stirring, until fragrant, about 30 seconds to 1 minute.
Add all remaining ingredients except the cornstarch and water; bring to a boil. Reduce heat to medium and cook for a minute or two. Mix the cornstarch with water, and add to the sauce, stirring until it bubbles and thickens.