In a large Dutch oven, sauté the chopped bacon in butter over medium heat until crisp and browned, about 3 to 5 minutes. Remove the bacon with a slotted spoon and set aside.
Pat the beef dry with a paper towel. Place the flour in a bowl or large zip-top bag and season with about 1/2 teaspoon of kosher salt and 1/2 teaspoon of pepper. Add the meat and toss to coat well. Remove the coated meat and discard any extra flour. Sear the beef in the butter and bacon drippings until browned on all sides, about 5 minutes per batch. Work in batches so you don't overcrowd the pan. Remove the meat from the pot.
Add the Guinness (or wine) and the vinegar to the pot. Cook over medium-high heat, using a wooden spoon to loosen any browned bits from the bottom. Add the bacon and meat back to the pot, along with the tomato paste, brown sugar, garlic, remaining 1 teaspoon of kosher salt, remaining 1/2 teaspoon of pepper, thyme, bay leaf, paprika, and broth. Stir really well to combine. Bring to a boil, then reduce the heat to a low simmer. Cover and cook, stirring occasionally, until the meat is tender, about 1 1/2 hours.
Add the onions and carrots and simmer, covered, for 10 minutes. Add the potatoes and mushrooms and simmer until the vegetables are tender, about 30 more minutes. Add extra broth at the end to thin the stew, if necessary.
Discard the bay leaf. Stir in the parsley and season with salt and pepper to taste. Ladle into bowls and serve. Garnish with additional fresh parsley, if desired.