Heat the oven to 250°F.
Park a large Dutch oven over high heat for 2 minutes.
While the pot is heating, rub the meat with 2 tablespoons of the salt. Add 1 tablespoon of ghee to the pot, then add the meat and sear on all sides until deeply browned — 2 to 3 minutes per side. Whatever you do, do not crowd the pan or the meat will boil rather than brown. If necessary, work in batches. As the meat is browned, move to a platter.
Kill the heat and allow the pot to cool for 2 minutes, then add the remaining tablespoon of ghee and return to medium heat. Add half the mushrooms and cook, stirring, for 2 minutes. Follow with half the carrots and half the onions along with all of the garlic, herbs de Provence, pepper, and remaining salt. Cook, stirring occasionally, until the garlic is aromatic — 2 to 3 minutes.
Add the tomato juice and vinegar, increase the heat to medium-high, and bring to a boil. Cook, scraping up any browned bits on the bottom of the pot, until the liquid has reduced by half — 3 to 5 minutes. Then return the meat to the pot and nestle it down into the vegetables. Cover, transfer the pot to the oven, and cook for 2 hours.
Carefully remove the pot from the oven and add the remaining mushrooms, carrots, and onions, along with all the potatoes. Cover and return to the oven until the vegetables are cooked through and the meat is fork-tender — 2 to 3 hours.
When the meat and vegetables are done, use a slotted spoon or spider to remove the hunks and chunks to a bowl. Filter the liquid through a sieve or into a fat separator, if desired. Return the filtered and defatted liquid to the Dutch oven and simmer over medium heat until the sauce reduces by one quarter — about 5 minutes. Kill the heat and return the meat and vegetables to the pot. Cool to room temperature then refrigerate overnight
When ready to serve, place the covered pot back in the oven then turn the oven to 350°F, allowing the roast to heat with the oven. In 45 minutes, the meat should be hot and the sauce bubbling. Serve directly from the pot to a grateful world.