In a bowl, toss pork with 1/4 cup soy sauce and ginger. Marinate 20 minutes. In another bowl, stir together remaining 2 tbsp. soy sauce, rice vinegar, cornstarch, sugar, and salt; set aside.
Heat peanut oil in a large pot (at least 5 qts.) over medium-high heat, then add pork and marinade. Cook, stirring constantly, until pork loses its pink color, about 4 minutes. Stir in bamboo shoots and cook 1 minute.
Increase heat to high, add broth, and bring to a boil. Add mushrooms, reduce heat to a simmer, and cook about 20 minutes. Add tofu and simmer 5 minutes. Add soy-vinegar mixture and simmer 5 minutes more; the liquid will thicken.
In a small bowl, beat eggs with sesame oil. Slowly pour eggs into soup in a thin stream while stirring soup very slowly in one direction. Add pepper, stir briefly, then simmer 5 minutes. Serve with cilantro and green onions.
Note: Nutritional analysis is per cup.