Simmer dried mushrooms in water for 15 minutes. Let sit for 1/2 hour, then drain through coffee filter or fine mesh sieve, squeezing juice from mushrooms. Reserve the liquid.
In a large, heavy-bottomed braising pan or Dutch oven, heat the oil to very hot. In batches, brown the short ribs. Remove them to a side platter. Add the onions and cook until lightly colored. Add the garlic and cook for 1 more minute. Return the short ribs to the pan and add the mushroom reconstituting water.
On low flame, cook for 1 hour and 15 minutes, occasionally re-positioning the ribs for even cooking until very tender.
Remove the ribs and strain the stock. Skim off most of the fat (you can do this by cooling it down, then setting it in the refrigerator). Bring stock to slow boil in the pan. Add all the mushrooms and meat. Simmer and heat through. Season with salt and pepper.
To serve, put soup into bowls. Place 2 ribs in center, scoop of barley to the side, and mushrooms around. Serve with Mustard-Horseradish Sauce.
Remove ribs and seeds from the chile and mince. Mix into horseradish and mustard.