Preheat the oven to 325 degrees. Heat a 6-to-8-quart Dutch oven over medium-high heat; add the bacon and cook until lightly browned. Remove with a slotted spoon to a large plate, leaving the drippings in the pot.
Pat the beef dry with paper towels; season with salt and pepper. Add the beef to the pot in a single layer (do this in batches); sear for 3 to 5 minutes, turning to brown all over. Transfer with a slotted spoon to the plate with the bacon.
Add the carrots and onions to the pot and cook until softened and slightly browned, 7 to 8 minutes. Season with salt and pepper. Meanwhile, make a "bouquet garni": Tie the thyme, bay leaf, garlic, parsley and celery together with twine (nestle the garlic in the celery stalk).
Return the bacon and beef to the pot. Add the flour and stir for a few minutes until the meat is coated. Stir in the tomato paste. Add the brandy and cook until reduced by half, about 5 minutes. Add the red wine; cook until reduced by half again, about 10 more minutes. Add the stock and bouquet garni; bring to a low boil. Stir gently, then cover and transfer to the oven; cook until the meat is tender and cooked through, stirring occasionally, about 1 hour 30 minutes.
Meanwhile, melt the butter in a medium skillet over medium heat. Add the pearl onions and cook until slightly softened, about 2 minutes. Add the sugar and 1/4 cup water; cook until the water evaporates and the onions are browned, about 5 minutes. Add the mushrooms; cook until slightly softened and golden, 3 to 4 minutes. Season with salt and pepper; set the skillet aside.
Remove the meat from the pot with a slotted spoon. Let the sauce sit for a few minutes, then skim off the fat and discard. Return the meat to the pot. Add the pearl onions and mushrooms; heat through. Season with salt and pepper and garnish with parsley. (For better flavor, make the dish a day ahead.)