Heat broth and wine in a saucepan set over medium heat until simmering. Add dried mushrooms; cover and let stand off heat for 10 minutes. Strain out mushrooms, reserving broth mixture; cool mushrooms slightly and chop finely.
Heat 2 tablespoons oil in an ovenproof pan set over medium-high heat. On a plate, combine flour and 1/2 teaspoons each salt and pepper. Toss beef in flour mixture and brown evenly in hot oil, working in batches. Remove from pan and set aside.
Add remaining oil, onion, garlic, rosemary, carrots, salt and pepper to pan; cook, stirring often, for 10 minutes or until vegetables are softened. Add fresh and dried mushrooms and brown for 5 minutes.
Return beef to pan along with any leftover flour. Stir in broth mixture, scraping up any browned bits from the bottom of the pan, and bring to a boil.
Reduce heat and simmer 1 hour, stirring occasionally until very tender. If serving right away, pour the stew into bowls, and garnish each with 1 tablespoon blue cheese and rosemary.