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

Cut the tofu into 1-inch cubes if you have not done it yet. Set the cubes on a plate lined with a clean towel or paper towels and press gently to dry the surface.

Put the soy sauce, rice vinegar, sugar, 1/2 cup water, and 1 tablespoon of the cornstarch into a small bowl. Stir until the cornstarch dissolves and the sauce looks smooth.

Put the tofu cubes into a medium bowl. Sprinkle the remaining 1 tablespoon cornstarch over the tofu and toss gently until the pieces are lightly coated on all sides.

Add the chow mein noodles to the boiling water in the pot. Cook them until just tender but still slightly firm in the center, following the package time and checking 1 minute early.

Drain the noodles in a colander. Shake off the extra water well and set the colander near the stove.

Set a large skillet or wok over medium-high heat. Let it heat for about 1 minute so the tofu will brown instead of steam.

Add 1 tablespoon of the oil to the hot skillet. Put the tofu into the skillet in one layer.

Cook the tofu for 3 to 4 minutes without moving it much, until the bottom looks golden.

Turn the tofu pieces with a spatula. Cook for 3 to 4 minutes more, until several sides are browned.

Transfer the browned tofu from the skillet to a plate.

Add 1 tablespoon of the oil to the same skillet. Put the mushrooms into the skillet and cook for about 3 minutes, stirring once or twice, until they start to shrink and brown at the edges.