Set a large wok or 12-inch skillet, a medium bowl, and a plate lined with paper towels near the stove.

Wrap the tofu in a clean kitchen towel or paper towels, set it on the counter, and place a heavy skillet or a few cans on top. Let it press for 10 minutes to remove extra moisture.

While the tofu presses, put the broccolini, oyster mushrooms, scallion whites, scallion greens, garlic, and ginger near the stove so everything is ready before cooking starts.

Put the soy sauce, black vinegar, and 1 tablespoon of the cornstarch into the medium bowl with 1/4 cup water. Whisk until the cornstarch is fully dissolved and the sauce looks smooth.

Unwrap the tofu and tear it into 1-inch pieces with rough edges. Put the tofu pieces into a dry bowl.

Sprinkle the remaining 2 tablespoons cornstarch over the tofu in the bowl. Toss gently until the tofu is lightly coated on all sides.

Warm the jasmine rice according to the package directions and keep it covered so it stays hot.

Pour 2 tablespoons of the oil into the wok or skillet and heat it over medium-high heat until the oil looks hot and loose in the pan.

Add the tofu to the skillet in a single layer. Cook for 3 to 4 minutes without moving it much, until the bottom is golden brown.

Turn the tofu pieces with tongs or a thin spatula. Cook for 3 to 4 minutes more, until the second side is browned and the edges look crisp. Transfer the tofu to the towel-lined plate.

Add the remaining 1 tablespoon oil to the same skillet. Put the broccolini into the skillet and cook for 2 minutes, stirring often, until it turns bright green.

Add the oyster mushrooms and the scallion whites to the skillet. Cook for 3 minutes, stirring often, until the mushrooms soften and the broccolini starts to become tender.