If using chuck roast and not already cut stew meat, cut the beef into 1-inch cubes, trimming off excess fat.
Place flour, salt and pepper in a large zip-top bag. Add the cubes of beef, seal the bag, and shake to coat the meat with the flour mixture. (Alternatively, you can place the beef, flour, salt and pepper in a large bowl and stir to coat the beef.)
In a large Dutch oven or other heavy pot, heat 1 tablespoon of the olive oil over medium heat. When the pot is hot, add half of the beef in a single layer. Let the beef brown on the first side for about 2 minutes, then flip and brown the other side. Transfer meat to a clean plate. Add another tablespoon olive oil to the pot. Brown the second half of the beef, about 2 minutes per side. (*Save any extra flour in the bag - you will add it to the pot later.) Remove the browned beef to the plate with the first half of the beef.
Add the remaining tablespoon of olive oil to the pot, followed by the onion and mushrooms. Sauté for 4-5 minutes, until the vegetables begin to soften.
Add the garlic, tomato paste, and any remaining flour from the bag. Cook, stirring, for 30 seconds to 1 minute.
Pour in the red wine and stock/broth. Stir, scraping up any browned bits from the bottom of the pot. Add the browned beef back to the pot (along with any juices from the plate). Then stir in the carrots, potatoes, Worcestershire sauce, Italian seasoning, thyme sprigs and bay leaf.
Bring stew to a simmer. Reduce the heat to maintain a low simmer, cover the pot, and cook for 1 ½ hours, until beef is tender, stirring occasionally.
Remove the bay leaf and thyme stems (the leaves will have fallen off). Taste and add additional salt and pepper if needed. Serve.