Put pork chops on a sheet of plastic wrap and wrap airtight. Freeze just until firm to the touch, at least 2 and up to 3 hours. Cut into very thin diagonal slices.
In a small bowl, soak mushrooms in chicken broth until soft and pliable, 20 to 30 minutes; occasionally work mushrooms with your fingers to release any grit. Lift mushrooms from broth, squeezing out liquid. Gently fold each mushroom in half, gill side out, and trim off any hard stems.
Pour 1/2 cup soaking broth into a measuring cup and set aside. Pour 1/4 cup broth into another measuring cup, leaving grit behind, and add water if needed to make 1/4 cup; stir in black bean sauce.
Meanwhile, trim ends from green vegetables. Peel broccolini stems, then cut into 3-in. lengths (if wider than 1/3 in., also halve lengthwise). Rinse and set aside. Cut remaining green vegetables into 3-in. lengths, separating clusters of bok choy into single stalks; rinse together and drain.
Set a wok or 5- to 6-qt. pan over high heat. When hot, pour in 2 tbsp. oil and swirl to coat. Add pork, onion, and ginger and fry, stirring occasionally, until meat is mostly cooked but still a bit pink, 1 to 1 1/2 minutes. Transfer ingredients to a plate with a slotted spoon.
Add broccolini stems, shiitakes, and reserved 1/2 cup soaking broth to pan and cover quickly. Cook until stems are barely tender-crisp, 1 to 2 minutes. Uncover and add remaining 1 tbsp. oil and rest of green vegetables. Cook, stirring, until leaves and flowers wilt, 1 to 1 1/2 minutes. Return pork mixture to pan along with reserved black bean liquid; cook until bubbling.
*Look for black bean garlic sauce in your supermarket's Asian-foods section. Buy Chinese broccoli and yu choy at a farmers' market or an Asian market.
Note: Nutritional analysis is per serving.