Finely chop or grate the cabbage, carrots, and garlic, then place them in a large mixing bowl. Add minced ginger and soy sauce, and stir to combine. Let sit for 10 minutes to soften and meld flavors.
Sprinkle the cornstarch and dried ginger powder over the vegetable mixture. Mix well until the ingredients hold together and form a sticky, cohesive dough.
Heat vegetable oil in a deep frying pan or wok over medium heat until shimmering and hot (~180°C/356°F). While the oil heats, shape the mixture into small balls about the size of a walnut, using damp hands to prevent sticking.
Carefully drop the shaped balls into the hot oil in batches. Fry for 4-5 minutes, turning occasionally, until they are golden brown and crispy on all sides. Use a slotted spoon to remove and drain on paper towels.
In a small saucepan, heat a teaspoon of oil over medium heat. Add finely chopped garlic and cook until fragrant, about 30 seconds. Pour in soy sauce, tomato ketchup, and rice vinegar, stirring to combine. Simmer for 2-3 minutes until slightly thickened.
Toss the crispy vegetable balls into the sauce or spoon the sauce over them. Stir gently to coat evenly, then cook for an additional minute to allow flavors to meld.
Transfer the coated vegetable balls to a serving platter. Garnish with chopped scallions for a fresh, bright finish. Serve immediately while hot and crispy.
