Whisk the egg white, 1 tablespoon cornstarch and 1 teaspoon soy sauce in a large bowl until frothy. Add the shrimp and toss to coat. Refrigerate 10 minutes. Meanwhile, whisk the hoisin sauce, vinegar and the remaining 1 tablespoon soy sauce and 2 teaspoons cornstarch in a small bowl, then whisk in the chicken broth. Set aside.
Drain the shrimp. Heat the vegetable oil in a wok or large skillet over medium-high heat, then stir-fry the scallion whites, ginger and garlic, about 30 seconds. Add the shrimp and stir-fry until almost cooked through, about 3 minutes. Add the cabbage and stir-fry until wilted and the shrimp are just cooked through, about 2 more minutes.
Stir the hoisin sauce mixture, then add to the wok and simmer, stirring occasionally, 2 minutes. Stir in the scallion greens. Serve with rice, if desired.