If you are using them, pour 1 cup of boiling water over the dried porcini mushrooms and allow them to rehydrate for 30 minutes. Remove the mushrooms and chop coarsely. Pour the soaking water through a paper towel (to remove any dirt or debris) into a bowl and set aside.
In a large sauté pan, pour enough water to cover the bottom by about 1/8 inch. Over medium heat, cook the salt pork in the pan until the water evaporates, stirring occasionally. Once the water is gone, reduce the heat to medium-low, and continue to cook the salt pork until much of the fat has rendered out of it. Add a tablespoon of butter and continue to cook the salt pork unti the pieces are browned and crispy. Use a slotted spoon to remove the salt pork pieces to a large Dutch oven or other large, thick-bottomed, lidded pot.
Increase the heat to medium-high. Working in batches so that you do not crowd the pan, brown the beef. Leaving space around each piece of sizzling meat ensures that it browns and does not steam. Don't move the pieces of beef in the pan until they get a good sear, then turn them so they can get browned on another side. Take your time. This will take 15-25 minutes, depending on how large a sauté pan you have. Once browned, remove the beef from the sauté pan and place in the Dutch oven with the salt pork.
When all the beef has browned, add the shallots, the one chopped carrot, and the chopped porcini mushrooms if using. Stir in the pot to remove any browned, stuck-on bits in the pan. Cook for 2-3 minutes, then add the garlic and the tomato paste. Cook another 2-3 minutes, stirring frequently.
Add the brandy and stir to combine. Boil down by half, then add the strained mushroom soaking water (if using). Scrape any remaining browned bits off the bottom of the sauté pan and pour the contents of the pan into the Dutch oven.
To the Dutch oven add the bottle of wine and enough beef stock to almost cover the beef; the beef pieces should be barely poking up out of the liquid. Add the parsley, bay leaves, thyme and cloves. Cover and bring to a bare simmer. After 1 hour, add the second carrot, peeled and cut into chunks of 1-2 inches. Continue cooking for another hour, or until the beef is tender.
Meanwhile, trim the tough stems off the shiitake, cremini, or button mushrooms and slice into 2-3 large pieces; small mushrooms leave whole. Prepare the pearl onions. Boil them in their skins for 4-5 minutes. Drain and submerge in a bowl of ice water. Slice the tips and root ends off the onions and slip off the outer skins.
When the beef is tender, use tongs to remove all the beef and the chunks of carrots; set aside in a bowl. Strain the contents of the Dutch oven through a fine-meshed sieve set over a medium pot. This will be the sauce. Boil the sauce down, tasting frequently. If it begins to taste too salty, turn off the heat. Otherwise, boil down until you have about 3 cups. Turn off the heat.
Heat a large sauté pan over high heat and add the mushrooms. Dry sauté the mushrooms over high heat, shaking the pan and stirring often, until they release their water, about 4-5 minutes. Add the pearl onions and 3 tablespoons butter and toss to combine. Sprinkle salt over the onions and mushrooms. Sauté until the onions begin to brown. Remove from heat.
Returning to the sauce, reduce the heat to medium and whisk in the beurre manie. Whisk in a third of the paste, wait for it to incorporate into the sauce, then add another third of the beurre manie, and so on. Do not let this boil, but allow it to simmer very gently for 2-3 minutes. Stir in the remaining 2 tablespoons of brandy. Taste for salt and add some if needed.
To serve, coat the beef, carrots, mushrooms and pearl onions with the sauce and serve with potatoes, egg noodles or lots of crusty bread.
