Set a 12-inch nonstick or well-seasoned skillet, a plate, and a small bowl near the stove. Line the plate with paper towels.

Put the tofu cubes on the towel-lined plate in an even layer. Lay more paper towels on top and press gently with your hands to remove extra moisture.

Leave the tofu to press for 5 to 10 minutes while you prepare the vegetables and sauce.

In the small bowl, stir together the soy sauce, rice vinegar, brown sugar, 1 tablespoon of the cornstarch, the black pepper, and the water until smooth. Set the bowl by the stove.

When the tofu has pressed, pat the top dry. Put the tofu in a medium bowl and sprinkle over the remaining 1 tablespoon cornstarch.

Toss the tofu gently in the bowl until the cubes are lightly coated all over. The coating should look thin and dry, not pasty.

Set the skillet over medium-high heat. Add 2 tablespoons of the neutral oil and heat until the oil looks loose and shiny.

Add the tofu cubes to the skillet in a single layer. Cook for 3 to 4 minutes, until the bottoms are golden brown.

Turn the tofu cubes with tongs or a thin spatula. Cook for 3 to 4 minutes more, until several sides are browned and the tofu looks firm and crisp at the edges.

Transfer the browned tofu from the skillet back to the paper towel-lined plate. Keep the skillet over medium-high heat.

Add the remaining 1 tablespoon oil to the skillet. Add the sliced mushrooms and cook for 3 minutes, stirring once or twice, until they soften and start to brown.

Add the broccoli florets and red bell pepper strips to the skillet. Cook for 3 to 4 minutes, stirring often, until the broccoli is bright green and just tender but still has some bite.