Set a large nonstick skillet on the stove. Place a large bowl, a small cup, and a plate near the skillet so they are ready when you need them.

Put the tofu cubes on a cutting board or tray and pat them very dry with paper towels. Dry tofu browns better and sticks less.

Put the tofu cubes into the large bowl. Sprinkle the cornstarch over the tofu.

Toss the tofu gently in the bowl until the cubes have a light, even coating. Set the bowl aside.

Pour the soy sauce and balsamic vinegar into the small cup and stir them together. Set the sauce near the stove.

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

Put half of the tofu into the hot skillet in a single layer. Leave space between the pieces so they can brown instead of steam.

Cook the first batch of tofu for 3 to 4 minutes without stirring, until the bottoms look deep golden.

Turn the tofu pieces with tongs or a thin spatula. Cook for 3 to 4 minutes more, turning once or twice, until several sides are browned and the coating looks crisp. Transfer the tofu to the plate.

Add the remaining 1 tablespoon oil to the skillet. Put the rest of the tofu into the skillet.

Cook the second batch of tofu for 6 to 7 minutes, turning once or twice, until the cubes are browned and crisp at the edges. Transfer the tofu to the plate with the first batch.

Put the sliced red onion into the same skillet. Cook for 2 minutes, stirring often, until it starts to soften.