Place tofu in pie plate and set heavy plate on top. Weight with 2 heavy cans; let stand at least 15 minutes (tofu should release about 1/2 cup liquid). Whisk 1 tablespoon soy sauce, sesame oil, and 1 teaspoon cornstarch in medium bowl; toss pork with marinade and set aside for at least 10 minutes (but no more than 30 minutes).
Combine 3 tablespoons cornstarch with 3 tablespoons water in small bowl and mix thoroughly; set aside, leaving spoon in 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.
Bring broth to boil in large saucepan set over medium-high heat. Reduce heat to medium-low; add bamboo shoots and mushrooms and simmer until mushrooms are just tender, about 5 minutes. While broth simmers, dice tofu into 1/2-inch cubes. Add tofu and pork, including marinade, to soup, stirring to separate any pieces of pork 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 soup, use 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 once to evenly distribute egg; ladle into bowls and top with scallions.