Thinly slice fresh shiitake mushroom caps, discarding tough stems. (Or soak dried shiitake mushrooms in warm water; cover until softened. Discard tough stems; thinly slice mushroom caps.)
Bring stock to a boil in a large pot over medium-high. Add pork and mushrooms; simmer until cooked through, 1 to 2 minutes.
Stir in vinegar, scallions, bamboo shoots, soy sauce, chile-garlic sauce (if using), sesame oil, and white pepper until combined; gently stir in tofu.
Stir together cornstarch and ¼ cup water in a bowl until smooth and no lumps remain.
Stirring gently and constantly, slowly pour cornstarch mixture in a steady stream into pot; cook until thickened, about 1 minute.
Remove from heat. Gently stir soup in 1 direction to create a whirlpool.
Slowly pour beaten eggs into soup in a thin stream to form egg drops.
Garnish with additional scallions (if using).
