Preheat oven to 350° F. Soak dried mushrooms in 2 cups boiling water.

Season ribs well with salt and pepper. Heat oil in a large, heavy pot 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, 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 ¼ inch to keep sediment out), 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 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, discard bones and large pieces of fat, then 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.

Refrigerate overnight. The next day, remove additional fat from the surface before reheating. Serve over polenta, sprinkled with gremolata.

Slow-cooker variation: After browning the meat, add it to a slow cooker, along with the rehydrated mushrooms and the rest of the ingredients, and cook on 'low' for 8 hours.

Mix ingredients in a small bowl and let sit at room temperature for an hour before serving.