Trim fat from pork; cut into 2 x 1/4-inch-wide strips. Combine pork, 2 tablespoons soy sauce, 2 teaspoons garlic, and 1 teaspoon ginger in a shallow bowl. Cover and marinate in refrigerator 2 hours.
Combine 1 tablespoon soy sauce, 2 teaspoons garlic, 1 teaspoon ginger, broth, hoisin sauce, and cornstarch in a small bowl; stir with a whisk. Heat oil in a large nonstick skillet over medium-high heat. Add 2 teaspoons garlic and crushed red pepper; stir-fry 30 seconds. Add mushrooms and onions; stir-fry 3 minutes. Add pork mixture and kale; stir-fry 3 minutes. Add broth mixture and bok choy; bring to a boil. Cook 1 minute or until mixture is thick. Serve over rice.