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 Ziploc bag and season with about 1/2 teaspoon of kosher salt and 1/2 teaspoon of pepper. Add the beef and toss to coat well. Shake off any excess flour.
Sear the beef in the butter and bacon fat over medium-high heat until browned on all sides, about 5 minutes. Work in batches so the pot isn't overcrowded. Remove the beef and set aside.
Pour the red wine and vinegar into the pot. Cook over medium-high heat, scraping the bottom with a wooden spoon to loosen any browned bits.
Return the bacon and beef to the pot. Stir in the tomato paste, garlic, remaining 1 teaspoon of kosher salt, remaining 1/2 teaspoon of pepper, thyme, bay leaf, paprika, and beef broth. Stir well to combine. Bring to a boil, then reduce heat to a low simmer.
Cover and cook, stirring occasionally, until the beef is very tender, about 1 1/2 hours. Stir in the onions and carrots; cover and simmer for 10 minutes. Add the potatoes and mushrooms; cover and simmer for about 30 more minutes, until the potatoes are fork-tender. Add a splash of extra broth at the end to thin the stew if needed.
Discard the bay leaf. Season with salt and pepper to taste. Ladle into bowls, garnish with chopped fresh herbs if desired, and serve.