Put a medium pot of water on the stove and bring it to a boil over high heat.

Mix the sauce: In a small bowl, stir together the soy sauce, ketchup, rice vinegar, brown sugar, and 2 tablespoons water until the sugar dissolves.

Set a large skillet or wok over medium-high heat and let it heat for about 1 minute.

Add 1 tablespoon of the neutral oil to the hot skillet and swirl it around the pan.

Brown the tofu: Put the tofu into the skillet in one layer. Cook without moving it for 3 to 4 minutes, until the bottom looks golden brown.

Turn the tofu pieces and cook for 4 to 5 minutes more, turning once or twice, until several sides are browned. Transfer the tofu to a plate.

Add the remaining 2 tablespoons oil to the same skillet.

Cook the vegetables: Put the onion and the scallion whites into the skillet. Cook for 2 minutes, stirring often, until the onion starts to soften.

Add the garlic and ginger to the skillet. Stir for about 30 seconds, until they smell fragrant.

Put the cabbage and carrots into the skillet. Cook for 4 to 5 minutes, stirring often, until the cabbage wilts and the carrots are just tender but still have a little bite.

Loosen the noodles: When the pot of water is boiling, add the yakisoba noodles. Cook for 1 minute, just until the strands loosen apart.

Drain the noodles in a colander and shake off the extra water.