Bring the broth to a boil in a medium saucepan; add in onion, green pepper and celery; simmer for about 5 minutes; remove the veggies with a slotted spoon and set aside.
Dissolve the cornstarch in cold water to make a paste and then add to simmering broth; stir to combine then add in the vinegar, reserved pineapple juice and soy sauce; mix to combine and simmer for about 2 minutes, or until sauce is thick and clear.
Season the sauce with black pepper or cayenne if desired.
In a large skillet or a large saucepan heat oil and saute the shallots and cabbage and well drained mushrooms for about 5-6 minutes (or until the cabbage is desired tenderness.
Add in the pineapple chunks, the veggies that were removed from the broth, along with the sauce and chicken or turkey; gently simmer until heated through.