Coat beef with flour:
Dry the beef cubes thoroughly using paper towels, then coat them evenly with seasoned all-purpose flour.Brown beef in batches:
In a Dutch oven over medium-high heat, warm the olive oil and butter. Working in batches, brown the beef on all sides, then transfer it to a plate and set aside.Cook onion and carrots:
Lower the heat to medium. In the same pot, cook the chopped onion and carrots until the onion turns translucent and lightly golden, roughly 5 minutes.Sauté garlic and paste:
Add the minced garlic and tomato paste, stirring for about 1 minute until aromatic.Deglaze with wine:
If using red wine, pour it in and scrape up any browned bits from the pot bottom, then let it simmer for 2 minutes.Add broth and beef:
Pour in the beef broth, return the browned beef to the pot, add the sliced mushrooms, thyme sprigs, and bay leaf. Stir everything together and bring to a gentle simmer.Simmer until tender:
Cover the pot and let the stew cook for 2 to 2.5 hours, or until the beef becomes fork-tender.Season and serve:
Discard the thyme sprigs and bay leaf. Season with salt and pepper to taste, then serve hot.