Heat sesame oil in a skillet over medium heat. Add garlic and ginger, and sauté for about 30 seconds until fragrant. Toss in the cabbage and mushrooms, cooking until soft—around 5–7 minutes. Add the crumbled tofu, scallions, tamari, rice vinegar, white pepper, and a pinch of salt. Cook for another 3 minutes, stirring constantly. Remove from heat and let cool.