Preheat the oven to 325 degrees F. In a Dutch oven, cook the bacon over medium heat until the fat is rendered; transfer to a platter. Pour all but 2 tablespoons of the fat into a heatproof cup and increase the heat to medium-high.
Working in batches, adding more bacon fat as needed, add the beef and cook until well browned, about 8 minutes; transfer to the platter.
Add the yellow onion, garlic, thyme and bay leaf to the pot and cook over medium heat, stirring often, until the onion is softened. Add the beef and bacon, sprinkle with the flour, season with salt and pepper and cook, stirring constantly, for 2 minutes. Stir in the wine and 2 cups water and bring to a boil. Cover, transfer to the oven and bake for 1 3/4 hours. Stir in the carrots and cook until the meat is very tender, 30 to 45 minutes.
Meanwhile, in a skillet, melt 2 tablespoons butter over medium-high heat. Add the mushrooms and cook until browned; transfer to a plate. Add the remaining 1 tablespoon butter and the pearl onions to the skillet and cook over medium heat until golden.
Transfer the beef and carrots to a bowl; cover. Let the braising liquid stand, then skim the fat from the surface. Return the beef and carrots to the liquid, add the mushrooms and onions and rewarm gently.