Add the cabbage, cucumber, carrots, onion, soy sauce, vinegar, sesame oil, lime juice as needed to taste, and half of the ginger. Mix well and let sit. Taste and adjust any of the ingredients as needed. Season with salt and pepper to taste before serving.
In a bowl whisk the mayo, remaining ginger and lime juice, garlic, cilantro. Season with salt and pepper to taste. Set aside.
Lightly toast the bread.
Spread the mayo mixture on both halves of the bread. Lay down the slaw mix, turkey, cheese, and tomatoes. Cut in half and serve with chips.