Cut beef into 2 to 2 1/2 inch pieces; pat with paper towels to absorb excess moisture. Combine 3 tablespoons flour, 1 teaspoon salt, paprika and pepper in a bowl; toss beef with flour mixture.
Cook beef in batches, in hot oil in a Dutch oven over medium-high heat, stirring often, 4-6 minutes 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 teaspoon salt. Bring to a boil. Cover, reduce heat to low, and cook, stirring occasionally, 1 hour.
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.
Whisk together remaining 1 tablespoon flour and 1/4 teaspoon 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.