Preheat oven to 450 ͒ F.
Pat the ribs dry, trim off and discard any excess fat. Sprinkle with salt and pepper, and arrange in a single layer in a roasting pan. Roast until the meat begins to brown, 15-20 minutes.
Use tongs to flip the ribs over, and arrange the onion, celery, carrot, and ginger around them and stir to coat the vegetables in fat. Spread the vegetables in an even layer. Roast an additional 15-20 minutes, until the ribs are well browned and the vegetables begin to turn golden. Reduce oven heat to 325 ͒ F.
Set the peppercorns, star anise, cinnamon stick, and 2 of the rosemary sprigs in a double-layered, 10-inch square of cheesecloth. Tie into a bundle with kitchen twine. Add the spice bundle, broth, Satsuma juice, and port to the roasting pan. Use a wooden spoon to scrape any browned bits from the bottom of the pan. Cover the roasting pan tightly with aluminum foil, and continue to cook until the meat is very tender, 2 to 2 1/2 hours.
Remove the roasting pan from the oven and reduce oven to 200 ͒ F. Use tongs to transfer the ribs to an oven-safe platter, cover, and return the ribs to the ribs to the oven to keep warm.
Set the roasting pan over two burners set on high heat on the stovetop. Bring the pan juices to a boil, and cook, stirring often, until the liquid has reduced to about 2 1/2 cups, about 10 minutes. Add the Satsuma slices to the pan and cook an additional minute.
Remove the platter of short ribs from the oven, and pour the pan sauce over them. Serve garnished with the remaining sprigs of rosemary, seasoning to taste with more salt and pepper.