Preheat oven to 300°F and adjust oven rack to lower-middle position and heat oven.
Pat the beef dry with paper towels and season with 2 teaspoons salt.
Heat 1 tablespoon oil in a large heavy-bottomed oven-safe pot over medium-high heat until hot. Add the chopped bacon and cook until crisp. Using a slotted spoon, remove from the pan, and set aside. Drain all, but 2 tablespoons of fat from the pot.
Add half of beef and cook, without moving, until well browned (about 4 to 6 minutes). Turn the beef and continue to cook on the second side until well browned, reducing heat if fat begins to smoke.
Transfer beef to a plate and repeat with remaining tablespoon oil and short ribs. Set the browned ribs aside on a dish.
Reduce the heat to medium, add the onions, celery, and carrots, and cook, stirring occasionally, until the onions are softened and beginning to brown, 10-12 minutes. (If onions begin to darken too quickly, add 1 to 2 tablespoons water to the pan.)
Add the mushrooms and cook until they release their liquid and the liquid cooks off. Add the garlic and cook another minute.
Add the flour and coat the mixture well. Cook, stirring constantly, until it browns on the sides and bottom of the pan, about 2 minutes.
Increase heat to medium-high, add wine, and simmer, scraping the bottom of the pan with a wooden spoon to loosen browned bits, until reduced by half, 8 to 10 minutes.
Add the stock, parsley, pepper, and bay leaf. Add cooked bacon, browned beef, and any accumulated juices to pot; cover and bring to simmer.
Transfer pot to oven and cook, until a fork slips easily in and out of meat, 2 to 2½ hours.
Using tongs, transfer meat to a cutting board and shred or cut into bite-sized pieces and return to the pot.
Taste for seasoning and add salt as needed before serving.
When browning the meat, work in batches so you don’t overcrowd the pan which will result in steaming the meat instead of searing.
To get a good sear, don’t move the ribs after adding to the pan for at least 3 minutes.
White or red wine are both good choices, but vermouth and dry sherry work too.
For a nonalcoholic option, use extra stock with two tablespoons of balsamic vinegar.
For extra richness replace the flour with tomato paste.
If the sauce doesn’t thicken enough, add a roux of butter and flour to thicken on the stovetop before serving.