1. Heat 2 tablespoons of olive oil in a large pot over medium-high heat. Add the beef cubes in batches, browning them on all sides. Remove the beef and set aside.
2. In the same pot, add the remaining tablespoon of olive oil and sauté the onions until translucent, about 5 minutes. Add the garlic and cook for another minute.
3. Return the beef to the pot. Stir in the beef broth and red wine, scraping up any browned bits from the bottom of the pot for extra flavor.
4. Add the carrots, potatoes, tomato paste, thyme, and bay leaf. Season with salt and pepper. Bring the mixture to a boil, then reduce the heat to low.
5. Cover the pot and let the stew simmer for 1.5 to 2 hours, or until the beef is tender and the flavors have melded together.
6. In a small pan, melt the butter and stir in the flour to create a roux. Cook for 1-2 minutes, then stir it into the stew to thicken the broth.
7. Remove the bay leaf before serving. Taste and adjust the seasoning as needed.

A little tip from Mama Lou: let the stew rest for about 15 minutes before serving to allow the flavors to fully develop. This was a trick she always swore by, and it makes a noticeable difference.