Press the tofu: Set a large nonstick skillet or well-seasoned wok and a plate near the stove. Wrap the tofu in a clean kitchen towel or paper towels, put it on the plate, and set a heavy pan or a few cans on top for 10 minutes to press out extra water.

While the tofu presses, cut the cabbage into thin strips, slice the bell pepper and onion, slice the scallions, and keep the white and green parts in separate small piles. Finely chop the garlic and grate or very finely chop the ginger.

Unwrap the tofu and cut it into 1-inch cubes.

Put the tofu cubes into a medium bowl. Add 1 tablespoon of the soy sauce and the cornstarch, then toss gently until the tofu is lightly coated.

Mix the sauce: In a small bowl, stir together the remaining 3 tablespoons soy sauce, the ketchup, rice vinegar, brown sugar, and water until smooth.

Place the skillet over medium-high heat and add 1 tablespoon of the oil. Let the oil heat for about 30 seconds.

Add the tofu to the hot skillet in a single layer. Leave it alone for 3 minutes so the first side can brown.

Turn the tofu pieces with tongs or a thin spatula. Cook for 3 to 4 minutes more, turning as needed, until several sides are golden brown and the coating looks set.

Transfer the browned tofu from the skillet to the plate.

Add the remaining 1 tablespoon oil to the same skillet. Swirl it around the pan.

Add the onion, bell pepper, cabbage, and the scallion whites to the skillet. Stir often for 4 to 5 minutes, until the cabbage starts to soften and the onion looks glossy.

Add the garlic and ginger to the skillet. Stir for 30 seconds, just until fragrant.