Preheat the oven to 325°F (163°C).
Season the beef cubes generously with salt and black pepper.
In a large Dutch oven or heavy-bottomed pot, heat 2 tablespoons of olive oil over medium heat.
Add the diced bacon and cook until crisp. Remove the bacon with a slotted spoon and set aside, leaving the fat in the pot.
Increase the heat to medium-high and brown the beef cubes in batches in the bacon fat, about 5 minutes per batch, ensuring a good sear on all sides. Remove browned beef and set aside.
Add the chopped onion and sliced carrots to the pot and cook until softened, about 5 minutes.
Add the minced garlic and tomato paste, stirring for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir well to combine. Cook for 2 minutes to remove the raw flour taste.
Slowly pour in the red wine, scraping the bottom of the pot to loosen any browned bits.
Add the beef broth, bouquet garni, browned beef, and cooked bacon back into the pot. Bring to a simmer.
Cover the pot with a lid and transfer it to the preheated oven. Cook for 2 hours, stirring occasionally.
While the stew cooks, prepare the pearl onions: bring a pot of water to a boil, add the pearl onions, and blanch for 2 minutes. Drain and peel the onions.
In a skillet, heat 1 tablespoon olive oil and 1 tablespoon butter over medium heat. Add the pearl onions and sauté until golden and tender, about 10 minutes. Remove and set aside.
In the same skillet, add the remaining 1 tablespoon butter and sauté the quartered mushrooms until browned and their moisture evaporates, about 8 minutes. Set aside.
After the stew has cooked for 2 hours, add the sautéed pearl onions and mushrooms to the pot. Stir to combine.
Return the pot to the oven and cook uncovered for an additional 1 hour, until the beef is very tender and the sauce has thickened.
Remove the bouquet garni. Taste and adjust seasoning with salt and pepper as needed.
Serve hot, garnished with chopped fresh parsley.