Preheat oven to 300°F. Pat the roast completely dry on all sides. Season evenly with the salt and pepper, pressing it into the surface. Heat a heavy Dutch oven over medium heat. Add robust EVOO. When shimmering, brown the roast deeply on all sides, including edges, until a dark crust forms. Remove the roast to a plate.
Lower heat slightly. Add the Garlic EVOO and using a wooden spoon, scrape up all the browned bits from the bottom of the pot. Then add the onions. Cook until softened and beginning to take on some colour. Add the carrots, celery, fennel, and mushrooms. Cook briefly, stirring to coat in the onion and pan juices. Add balsamic and simmer for 5 minutes, stirring once. Return the roast to the pot, nestling it into the vegetables. Add stock around the meat until the liquid comes halfway up the roast. Cover tightly and transfer to the oven. Cook 3 to 4 hours until fork-tender and the meat yields without resistance. Turn once halfway through.
Transfer the roast to a platter and tent loosely with foil. Simmer the liquid and vegetables uncovered until slightly reduced and glossy. The vegetables will be very tender. Taste and adjust seasoning.
To serve, slice across the grain or serve in large pieces, spooning vegetables and sauce where desired.
