Preheat oven to 200 degrees F. In large bowl mash tofu with a fork. Add carrot, green onions, cilantro, mint, garlic, flour, and 2 tablespoons of the soy sauce; stir to combine.
In a large skillet heat oil over medium heat. Tightly pack some of the tofu mixture into a 1/4-cup metal measuring cup. Unmold into the hot skillet by tapping measuring cup in bottom of skillet. Repeat to make 5 patties. Cook for 3 to 4 minutes per side or until browned and heated through. Remove to a baking sheet; keep warm in oven while cooking remaining 5 patties.
To serve, top tofu cakes with cucumber and mango. Serve with mint and Dipping Sauce. Makes 10 appetizers.
Stir together soy sauce, rice vinegar, and chili garlic sauce.