Preheat the oven to 325°F.
Season the beef cubes with salt and freshly ground black pepper.
Heat 1 tablespoon vegetable oil in a large oven-safe Dutch oven over medium-high heat.
Brown the beef cubes in batches until golden brown on all sides, then transfer to a plate and set aside.
Add more oil if needed, then add the chopped onion, carrots, and celery. Saute for 5 to 7 minutes, stirring occasionally, until the vegetables are softened.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the all-purpose flour over the vegetables and cook, stirring, for 1 minute to coat.
Stir in the tomato paste and cook, stirring, for 1 minute.
Pour in the red wine, scraping up any browned bits from the bottom of the pot.
Add the beef broth, bring to a gentle simmer, and cook until the sauce thickens slightly.
Return the beef cubes to the pot, add the bay leaf and fresh thyme sprigs, then stir and season with salt and pepper to taste.
Cover with a lid and transfer to the oven. Bake for 2 hours.
If using, stir in the sliced mushrooms, cover again, and bake for an additional 30 to 45 minutes, until the beef is very tender and the sauce is thick and rich.
Remove the bay leaf and thyme sprigs. Taste and adjust seasoning if needed.
Serve with creamy mashed potatoes, crusty bread, and steamed green vegetables.