Combine soy sauce, rice wine, brown sugar, and cornstarch in a small bowl until smooth; set aside.

Heat oil in a wok or skillet over medium-high heat. Stir-fry ginger and garlic until fragrant, about 30 seconds. Add steak and stir-fry until evenly browned, about 2 minutes. Stir in snow peas and cook until crisp-tender, about 3 minutes. Pour in soy sauce mixture and bring to a boil, stirring constantly. Reduce heat to medium-low and simmer until sauce is thickened and smooth. Serve immediately.