Heat the oven to 325°F. Set a 6 to 7 quart Dutch oven over medium heat and cook the bacon until golden and the fat has rendered, about 8 minutes. Remove with a slotted spoon and set aside, leaving the 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 and transfer to the oven. Braise for 2 ½ to 3 hours, until the beef falls apart under light pressure from a fork.
About 20 minutes before the stew is done, melt the butter in a large skillet over medium heat. Cook the pearl onions until browned in spots, about 8 minutes. Add the mushrooms and cook until browned and their liquid has evaporated, about 8 minutes more.
Remove the bay leaves and thyme stems from the stew. Fold in the mushrooms and pearl onions, taste and adjust the salt, and scatter the parsley over the top before serving.