Heat 1 teaspoon olive oil in a large Dutch oven over medium-high heat. Add mushrooms, and sauté for 5 minutes or until mushrooms begin to brown. Spoon mushrooms into a large bowl. Lightly coat pan with cooking spray. Add onion; sauté 10 minutes or until tender and golden brown. Add garlic; sauté 1 minute. Add onion mixture to mushroom mixture.
Place flour in a shallow bowl or pie plate. Dredge beef in flour, shaking off excess. Heat remaining 2 teaspoons oil in pan over medium-high heat. Add half of beef mixture; sprinkle with 1/8 teaspoon salt. Cook 6 minutes, browning on all sides. Add browned beef to mushroom mixture. Repeat procedure with remaining beef mixture and 1/8 teaspoon 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 potato and carrot. Simmer, uncovered, 1 hour and 15 minutes or until beef and vegetables are very tender and sauce is thick, stirring occasionally. Stir in remaining 1/2 teaspoon salt and pepper. Discard bay leaf. Garnish with thyme sprigs, if desired.