Measure flour and salt into a large plastic bag. If shanks are damp, pat dry with paper towels. Add 1 shank to bag. Shake to coat. Remove to a large platter. Repeat with remaining pieces. Save excess flour.
Lightly coat a large wide saucepan with oil and set over medium-high heat. When hot, add 2 or 3 shanks. Brown on all sides, 3 to 4 minutes. Add oil as needed. If pan gets too hot, reduce heat to medium. Remove each shank to a large plate as it is browned. Repeat with remaining shanks.
Meanwhile, slice onions in half. Place cut side down on cutting board and slice into thin strips.
After removing shanks from pan, reduce heat to medium.
Add onions, ginger and a little more oil.
Stir often until onion softens, 3 to 4 minutes.
Sprinkle with reserved flour mixture and stir until evenly mixed.
Gradually stir in sherry. Using a wooden spoon, scrape up and stir in any brown bits from pan bottom.
Stir in broth, teriyaki, chili flakes, sesame oil, star anise and mushrooms.
Bring to a boil, stirring often.
Return shanks to pan. Reduce temperature to medium-low.
Cover and simmer, turning shanks occasionally, until tender and meat is almost falling from bone, approximately 3 hours. Serve with sauce drizzled overtop.
Note: I use 1/2 cup fresh ginger and 2 teaspoons chili flakes. Port or marsala wine can be used instead of sherry. Enjoy!