Combine ginger and 2 tablespoons lime juice, and set aside to marinate for a minimum of 2 hours.
Dry-roast sesame seeds in large skillet over medium-low heat until fragrant, about 3 minutes, stirring constantly to prevent burning. Remove from heat, and set aside.
Heat oil in same skillet over medium heat, and sauté garlic slices until brown, about 2 minutes. Remove from heat, and set aside.
Squeeze lime juice from ginger. Combine ginger, tomato, cabbage, peanuts, garlic, remaining oil, and sesame seeds. Add soy sauce and remaining lime juice. Sprinkle with chickpea flour and toss. Garnish with finely chopped chilies, if using.