Place the beef stew cubes into a large mixing bowl and pour in 2 cups of red wine, ensuring the meat is fully submerged. Cover the bowl tightly and refrigerate, allowing the beef to marinate for at least 2 hours or preferably overnight to infuse maximum flavor.
When ready to cook, preheat the oven to 300°F (150°C). Remove the beef from the marinade, reserving the liquid for later use. Pat the beef pieces dry thoroughly with paper towels and season generously with salt and pepper.
In a large Dutch oven or heavy-bottomed pot, heat the olive oil over medium-high heat. Working in batches to prevent overcrowding, sear the beef until it is well-browned on all sides. Transfer the browned beef to a plate and set aside.
In the same pot, add the butter, followed by the chopped onions and carrots. Sauté the vegetables until they become tender and slightly golden, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Sprinkle the flour over the sautéed vegetables and stir continuously, cooking for 2–3 minutes until a golden roux forms. Gradually whisk in the reserved marinade, the remaining 2 cups of red wine, and the beef broth, ensuring the mixture is smooth and lump-free.
Incorporate the tomato paste, minced thyme, and bay leaves, bringing the mixture to a gentle simmer. Return the browned beef cubes to the pot, stirring in the sliced mushrooms to combine.
Cover the Dutch oven and transfer it into the preheated oven. Roast for 2 to 2½ hours, until the beef is fork-tender and the sauce is thickened and rich.
Remove the bay leaves before serving. Taste and adjust seasoning with additional salt and pepper if necessary. Garnish with chopped fresh parsley and serve hot over creamy mashed potatoes, buttered egg noodles, or alongside slices of crusty bread for a hearty, comforting meal.