Preheat oven to 350 degrees for 3 hours, or 275 for 5 hours. Soak dried mushrooms in 2 cups boiling water.
Season ribs well with salt and pepper. Heat oil in large, heavy pot (I used a 5-qt. enameled cast iron dutch oven) over medium heat until shimmering. Brown ribs in batches for 2-3 minutes per side, then set aside.
Pour out all but 1 tablespoon of accumulated fat from pot (if any), then sauté onion, carrots and celery until soft. Add garlic and stir until fragrant.
Create a hot spot in the pot by moving vegetables aside and leaving about a 3-inch radius bare. Add tomato paste and anchovy paste to the hot spot and stir vigorously until caramelized, then stir into the vegetables.
Add red wine to deglaze and cook until liquid is reduced by half.
Add tomatoes, mustard, Worcestershire sauce, mushrooms and soaking liquid (minus the last 1/4 inch to keep sediment out of your dish), plus herbs.
Add ribs to pot and fill with chicken stock or water until ribs are nearly covered. Bring liquid to a boil, then cover tightly and braise in oven for at least 3 hours at 350 or 5 hours at 275 or until ribs are fall-apart tender.
Remove ribs from liquid and set aside until cool enough to handle. Remove bay leaves and discard. While ribs cool, purée the braising liquid with an immersion blender until thick and set over medium-low heat to reduce if the sauce seems thin.
When ribs have cooled down shred the beef and return it to the pot. Remove from heat and cool to room temperature, skimming any large pools of fat from the surface.
Cook Polenta according to directions and add parmesan at the end of cooking, stir to combine. Spoon a generous helping of Polenta on a plate and top with Short Rib mix, top with diced fresh rosemary or parsley.