Whisk glaze ingredients in small bowl; whisk sauce ingredients in separate small bowl. In third small bowl, mix garlic and ginger with 1 teaspoon vegetable oil. Set bowls aside.
Heat 3 tablespoons vegetable oil in 12-inch nonstick skillet over medium-high heat until shimmering. While oil is heating, sprinkle cornstarch evenly into baking dish. Place tofu on top of cornstarch and turn with fingers until evenly coated. When skillet is hot, add tofu in single layer and cook until golden brown, 4 to 6 minutes. Turn tofu with tongs and cook until second side is browned, 4 to 6 minutes more. Add glaze ingredients and cook, stirring, until glaze is thick and tofu is coated, 1 to 2 minutes.