Place a large Dutch oven over medium heat. Add the bacon and cook for approximately 8 minutes, or until browned and the fat has rendered. Transfer the bacon to a plate with a slotted spoon, leaving the rendered fat in the pot.
Pat the beef cubes completely dry and season with the salt and pepper. Working in three batches so the pot is never crowded, sear the beef until deeply browned on all sides, about 6 minutes per batch. Transfer each batch to a plate.
Add the onion and carrots to the pot and cook until the onion softens and turns golden, about 6 minutes. Add the garlic and cook 1 minute more.
Stir in the tomato paste and cook for 2 minutes, until it darkens to a brick color.
Return the beef and bacon to the pot with any juices. Sprinkle the flour over everything and stir for 2 minutes.
Pour in the wine, scraping the bottom of the pot to release the browned bits. Add the beef broth, thyme sprigs, and bay leaves. The liquid should nearly cover the meat. Bring to a simmer.
Cover the Dutch oven, reduce the heat to low and simmer on the stovetop for approximately 3 hours. Check the pot every 45 minutes, stirring gently and adding a splash of beef broth if the liquid falls below the meat.
Remove the bay leaves and thyme stems from the stew. Fold in the mushrooms and taste and adjust the salt, and scatter the parsley over the top before serving.