Drain then press the tofu for 5-10 minutes to release excess moisture.
Heat 1 tablespoon of sesame oil in a large skillet over medium heat. Crumble the tofu with your hands and add it to the skillet.
Cook the tofu for 10-15 minutes, until it is starting to brown on the edges. Let it sit for 3-4 minutes at a time to get a sizzle/browning on one side before flipping it.
Move the tofu over to one side of the skillet, and on the other side add the mushrooms, carrots, cabbage, ginger, garlic, green onion, and 2 tablespoons of soy sauce.
Cook the egg roll filling over medium heat for 10 minutes, stirring occasionally.
Add 2 more tablespoons of soy sauce and 1 tablespoon of sesame oil to the pan once the veggies are mostly cooked down.
Stir and continue cooking for 5 minutes, or until the vegetables reach your desired softness.