Combine first 5 ingredients, stirring until sugar dissolves; set aside.
Spread tofu in a single layer onto several layers of paper towels; cover with additional paper towels. Let stand 15 minutes, pressing down occasionally.
Heat oils in a large nonstick skillet over medium-high heat. Add onion, garlic, and chiles; sauté 3 minutes. Add tofu; cook 8 minutes or until lightly browned, stirring occasionally. Stir in juice mixture; cook 1 minute or until heated. Remove from heat; stir in basil and mint. Spoon about 1/2 cup tofu mixture into each cabbage leaf.