Set a large wok or 12-inch skillet over medium heat and place a plate next to the stove for the cooked tofu.

Put the tofu cubes in a medium bowl. Sprinkle 1 tablespoon of the cornstarch over the tofu and toss gently until the cubes are lightly coated.

In a small bowl, stir together the soy sauce, black vinegar, brown sugar, red pepper flakes, the remaining 1 tablespoon cornstarch, and 1/3 cup water until smooth.

Check that the napa cabbage is sliced, the carrots are cut, and the scallion whites and greens are separated so everything is ready before the pan gets hot.

Increase the heat under the skillet to medium-high. Add 2 tablespoons of the oil and let it heat until it looks loose and shiny.

Put the tofu into the skillet in a single layer. Cook for 3 to 4 minutes, leaving it mostly undisturbed, until the bottom sides are deep golden.

Turn the tofu pieces with tongs or a thin spatula. Cook for 3 to 4 minutes more until several sides are browned and the tofu feels firmer. Transfer the tofu to the plate.

Add the remaining 1 tablespoon oil to the same skillet. Put the scallion whites, garlic, and ginger into the skillet and stir for about 30 seconds, just until fragrant.

Add the carrots to the skillet. Stir-fry for 2 minutes until they start to soften but still look bright.

Add the napa cabbage to the skillet. Stir-fry for 2 to 3 minutes until the cabbage wilts down but still keeps a little crunch in the thicker white parts.

Stir the sauce in the bowl again so the cornstarch is evenly mixed. Pour the sauce into the skillet.

Cook the sauce for 1 to 2 minutes, stirring often, until it thickens into a glossy coating and no dry cornstarch streaks remain.