1. Cut beef into 2- to 2 1/2-inch pieces; pat with paper towels to absorb excess moisture. Combine 3 Tbsp. flour, 1 tsp. salt, paprika, and pepper in a bowl; toss beef with flour mixture.
2. Cook beef, in batches, in hot oil in a Dutch oven over medium-high heat, stirring often, 4 to 6 minutes or until brown. Remove beef from Dutch oven. Add red wine, stirring to loosen particles from bottom of Dutch oven. Return beef to Dutch oven; add broth, thyme, bay leaf, and 1/2 tsp. salt. Bring to a boil. Cover, reduce heat to low, and cook, stirring occasionally, 1 hour.
3. Meanwhile, peel turnip, and cut into 1-inch cubes. Halve mushrooms. Add turnip, mushrooms, and carrots to stew. Cover and cook, stirring occasionally, 1 to 1 1/2 hours or until meat is fork-tender.
4. Whisk together remaining 1 Tbsp. flour and 1/4 tsp. salt until blended; whisk 1/2 cup hot broth into flour mixture until smooth. Whisk flour mixture into stew until smooth. Cook, stirring often, 20 minutes or until thickened.
*Beef broth may be substituted.