Set a large nonstick skillet over medium heat so it is ready when you start cooking.

Lay the tofu strips on a clean kitchen towel or paper towels. Press gently to remove extra moisture so the tofu browns instead of steaming.

Make the sauce: In a small bowl, stir together the soy sauce, 2 tablespoons of the hoisin sauce, the rice vinegar, the sesame oil, the cornstarch, and 1/4 cup water until smooth.

Put the beaten eggs in a small bowl near the stove. Keep the sliced scallion whites and greens in separate piles.

Cook the eggs: Add 1 tablespoon of the neutral oil to the hot skillet. Pour the eggs into the skillet and cook over medium heat for about 1 minute, stirring gently, until they are softly set and no longer look wet.

Transfer the eggs to a plate. Break them into large bite-size pieces with the side of a spoon or spatula.

Brown the tofu: Return the skillet to medium-high heat. Add 1 tablespoon of the neutral oil, then put the tofu into the skillet in a mostly even layer.

Cook the tofu for 3 to 4 minutes without moving it much, until the bottom looks golden in spots. Turn the pieces and cook for 2 to 3 minutes more, until the second side is browned.

Transfer the browned tofu to the plate with the eggs.

Cook the vegetables: Add the remaining 1 tablespoon of neutral oil to the same skillet. Put the mushrooms into the skillet and cook over medium-high heat for 3 to 4 minutes, stirring now and then, until they soften and their moisture cooks away.

Add the scallion whites to the skillet. Stir for about 30 seconds, until they smell fragrant.

Put the coleslaw mix into the skillet. Cook for 2 to 3 minutes, tossing often, until the cabbage wilts down but still has a little crunch.