In a 5-quart Dutch oven, cook bacon over medium heat until browned and crispy. Remove to a side dish with a slotted spoon and increase the heat to medium-high.
In 2 batches, brown the beef on all sides. Transfer each batch of beef to a large plate as it's browned. Drain all but 2 tablespoons of fat from the Dutch oven.
Reduce the heat to medium and add the onion. Cook, stirring, until softened, about 3 to 4 minutes. Add the flour and cook, stirring constantly, for 1 minute. Add the tomato paste, garlic, thyme and bay leaf and cook, stirring, for 2 minutes. Stir in the wine. Return the beef and half of the bacon to the Dutch oven and bring to a simmer.
Cover Dutch oven and set in lower third of oven to cook for 1 hour and 30 minutes. Turn beef over and add the carrots. The stew should be saucy, so add a little water if necessary. Continue to cook, covered, in the oven for 30 minutes.
Heat 1 tablespoon butter in a 10-inch skillet over medium heat. Add onions and cook, stirring, for about 4 to 5 minutes, until browned. Add the browned onions to the Dutch oven and continue to cook, covered, for 15 to 20 minutes or until the beef and vegetables are tender. Remove and discard thyme sprigs and bay leaf.
Meanwhile, wipe out skillet and add remaining 1 tablespoon butter over high heat. Add mushrooms and cook, stirring occasionally, for 4 to 5 minutes, until browned. Stir the mushrooms into the stew. Garnish with remaining cooked bacon and parsley and serve with mashed potatoes or noodles, as desired.