Start the tofu: Put a large nonstick skillet or wok on the stove over medium-high heat. Set a large plate next to it so you have a place to move the tofu later.

Drain the tofu well and pat it dry with paper towels or a clean kitchen towel. Cut it into 3/4-inch cubes so the pieces cook at the same rate.

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

In a small bowl, stir together the remaining 2 tablespoons soy sauce, the remaining 1 tablespoon cornstarch, the rice vinegar, the sugar, and 1/2 cup water. Stir until the cornstarch is fully mixed in, then set the bowl near the stove.

Add 1 tablespoon of the neutral oil to the hot skillet. When the oil looks shiny, add the tofu in a single layer.

Cook the tofu for 3 to 4 minutes without moving it much, until the bottom looks golden brown and releases easily from the pan.

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 looks firmer. Transfer the tofu to the plate.

Cook the vegetables: Add 1 tablespoon of the neutral oil to the same skillet. Add the cauliflower florets and spread them into an even layer.

Cook the cauliflower for 3 minutes, stirring once, until a few edges begin to brown.

Add 2 tablespoons water to the skillet and cover it with a lid or a sheet pan for 2 minutes. Uncover when the cauliflower is brighter in color and just starting to feel tender when pierced with a fork.

Add the remaining 1 tablespoon neutral oil to the skillet. Add the mushrooms and cook for 4 minutes, stirring now and then, until they give off their liquid and start to brown.

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