Heat oil in a large saucepan over high heat. Add garlic and ginger. Cook until fragrant and lightly browned, about 2 minutes. Stir in shrimp. Saute until opaque, about 3 minutes. Transfer shrimp to a bowl.
Pour chicken stock into the saucepan and bring to a boil. Reduce heat to medium; add tofu, asparagus, salt and cayenne pepper. Reduce heat to a simmer. Stir cornstarch into a bowl with enough water to form a thin paste. Stir into the soup and continue to simmer until clear and thickened, about 1 minute more. Stir shrimp back into soup and serve.