To make the sauce: Stir together broth, bean paste, soy sauce, and kosher salt. Set aside.
To poach the tofu: Slide tofu into a saucepan of simmering water and keep at a bare simmer while stir-frying rest of dish.
To stir-fry the pork: Heat a wok or large heavy skillet over high heat until hot and add 1 1/2 tablespoons corn oil, swirling to coat. Add pork and stir-fry, breaking up lumps and adding remaining 1/2 tablespoon corn oil if meat sticks, until no longer pink. Add garlic and ginger and stir-fry over moderate heat until very fragrant, about 2 minutes.
To finish the stir-fry: Stir reserved sauce, then add to pork and bring to a simmer. Drain tofu in a large sieve and slide into sauce, stirring gently.
Stir cornstarch mixture and add to stir-fry. Bring to a boil, stirring gently, and cook until thickened and glossy, about 15 seconds.
Turn off heat and sprinkle with sesame oil, sansho powder, to taste, and 2 tablespoons scallion. Stir once or twice, then serve sprinkled with remaining tablespoon scallion.