Heat 1 teaspoons olive oil in a large skillet over medium high heat. Add mushrooms, and sauté for 5 minutes or until mushrooms begin to brown. Spoon the mushrooms into a large bowl. Lightly coat the skillet with cooking spray. Add onion; sauté 10 minutes or until tender and golden brown. Add the garlic; sauté 1 minute. Add the onion mixture to the mushroom mixture.
Put flour in a shallow bowl or pie plate. Dredge the beef pieces in flour, shaking off excess. Heat remaining 2 teaspoons of oil in skillet over medium high heat. Add half of the beef mixture; sprinkle with 1/8 teaspoons salt. Cook 6 minutes, browning on all sides. Add browned beef to mushroom mixture. Repeat procedure with remaining beef mixture and 1/8 teaspoons salt.
Add 1 cup wine to pan, scraping pan to loosen browned bits. Add thyme, broth, and bay leaf. Bring to a boil. Stir in beef mixture. Cover, reduce heat to medium low, and simmer for 1 hour or until beef is just tender.
Stir in potatoes and carrots. Simmer, uncovered, 1 hour and 15 minutes or until beef and vegetables are really tender and sauce is thick, stirring occasionally. Stir in remaining 1/2 teaspoons salt and pepper. Discard bay leaf. Garnish with thyme sprigs, if you are using. Enjoy!