Place tofu in pie plate and set heavy plate on top. Place 2 heavy cans on top of the plate and let stand at least 15 minutes (tofu should release about 1/2 cup liquid).
In a medium bowl, whisk together 1 tablespoon soy sauce, sesame oil, and 1 teaspoon cornstarch. Add the pork and set aside for at least 10 minutes (but no more than 30 minutes).
In a small bowl, combine 3 tablespoons cornstarch with 3 tablespoons water; set aside, leaving spoon in bowl.
In a separate small bowl, mix remaining 1/2 teaspoon cornstarch with remaining 1 teaspoon water in small bowl; add egg and beat with fork until combined; set aside.
In a large saucepan over medium-high heat, bring chicken broth to a boil. Reduce heat to medium-low, add the bamboo shoots and mushrooms and simmer until mushrooms are just tender, about 5 minutes.
While the broth is simmering, dice tofu into 1/2-inch cubes. Add tofu and pork, (including marinade) to soup, stirring to separate any pieces that stick together. Continue to simmer until pork is no longer pink, about 2 minutes.
Stir cornstarch mixture to recombine. Add to soup and increase heat to medium-high; cook, stirring occasionally, until soup thickens and turns translucent, about 1 minute. Stir in vinegar, chili oil, pepper, and remaining 3 tablespoons soy sauce; turn off heat.
Without stirring the soup, use a soupspoon to slowly drizzle very thin streams of egg mixture into pot in circular motion. Let soup sit 1 minute, then return saucepan to medium-high heat. Bring soup to gentle boil, then immediately remove from heat. Gently stir soup to evenly distribute egg. Ladle into bowls and top with scallions.