Set a large nonstick skillet or a seasoned wok and a dinner plate by the stove. If you are serving the stir-fry with rice, warm the rice now so it is ready at the end.

Pat the tofu dry with paper towels or a clean towel. Tear it into rough 1-inch pieces so the edges stay uneven and can brown well.

Put the tofu on the plate and press it gently with more towels for 5 minutes to remove some moisture.

Put the chili bean paste, soy sauce, cornstarch, sugar, sesame oil, and 1/2 cup water in a small bowl. Stir until the cornstarch dissolves and the sauce looks smooth.

Cut the eggplant into 3/4-inch chunks if you have not already. Keep the scallion whites and greens in separate small piles so they are easy to add at different times.

Pour 2 tablespoons of the neutral oil into the skillet. Set the skillet over medium-high heat and heat the oil for about 1 minute, until it looks hot and moves easily across the pan.

Add the tofu to the skillet in one layer. Cook for 4 to 5 minutes, leaving it mostly undisturbed, until the bottom sides are golden brown.

Turn the tofu pieces with tongs or a spatula. Cook for 3 to 4 minutes more, until the second side has browned spots, then transfer the tofu back to the plate.

Add the remaining 1 tablespoon of neutral oil to the same skillet. Put the eggplant into the skillet and cook for 4 minutes, stirring every minute, until it starts to soften and pick up some color.

Add the mushrooms and the scallion whites to the skillet. Cook for 4 to 5 minutes, stirring often, until the mushrooms shrink down and the eggplant is tender when pierced with a fork.

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

Stir the sauce in the bowl again so the cornstarch does not stay on the bottom. Pour the sauce into the skillet and scrape in all of it.