Pat the beef chunks dry with paper towels and season generously with salt and pepper. Heating the olive oil in a large Dutch oven over medium-high heat, sear the beef in batches until deeply browned on all sides, then transfer to a plate.
Lower the heat to medium. Add the chopped yellow onion to the pot and sauté for 5 minutes until softened. Stir in the minced garlic and tomato paste, cooking for 1 additional minute.
Sprinkle the flour over the onion mixture, stirring continuously for 1 minute. Pour in the dry red wine, scraping up any browned bits from the bottom of the pot to deglaze.
Return the browned beef and any accumulated juices to the pot. Pour in the beef broth and add the fresh thyme. Bring the mixture to a gentle simmer.
Cover the Dutch oven, reduce the heat to low, and let it simmer gently for 1.5 hours, stirring occasionally.
Stir in the sliced carrots, halved baby potatoes, peeled pearl onions, and quartered mushrooms. Cover and continue to simmer for another 1 hour, or until the beef is fork-tender and the vegetables are fully cooked.
Remove from heat. Skim off any excess fat from the surface, adjust the salt and pepper to taste, and serve hot in deep bowls.