In a bowl, pour the hot coffee over the dried porcini mushrooms and leave to steep. When cool, drain, reserving the soaking liquid, and chop the mushrooms finely.
Preheat the oven to 325 degrees F.
Cut the beef into 2-inch cubes and toss with 1/2 teaspoon salt and some pepper. Heat a large wide-bottomed saucepan over medium-high heat and add a thin film of canola oil. Brown the beef in the oil in two or three batches, giving the meat some space. Add the browned meat to a bowl or baking dish as you go. Once all the beef is browned, pour off the excess grease, and add the red wine and Madeira to the pan. Cook until reduced by a third, about 3 minutes; then pour the wine over the meat. Set aside.
Add the butter, onions and 1/2 teaspoon salt to the saucepan. Cook until the onions are soft and brown, about 20 minutes. Add the celery and the shiitake and cremini mushrooms. Season with salt and pepper, and cook, stirring, until the vegetables wilt, 10 minutes. Add the sweet paprika, smoked paprika, thyme, cloves and tomatoes, as well as the porcini mushrooms and their soaking liquid (leave any grit behind in the bowl). Cook, stirring, for 5 minutes. Add the bay leaves and beef stock, and the browned beef and all the juices from the bowl. Bring to a simmer.
Cover the pan and transfer it to the oven. Bake for 1 hour; then lower the heat to 300 degrees and bake until the meat is very tender, about 2 hours longer. Serve in bowls, topped with dollops of Horseradish Cream.
Whip the cream in a cold metal bowl until soft peaks form. Add the horseradish, sour cream, salt, sugar, cayenne and vinegar, and stir to combine.