In a 5- to 6-qt. slow cooker, stir together the tomato paste, vinegar and flour until blended. Season the beef generously on all sides with salt and pepper, then add to the slow cooker and turn to coat. Scatter the carrots, potatoes, mushrooms, garlic and rosemary around the meat; season generously with salt and pepper. Cook on low heat until the meat is tender, about 8 hours.
Discard the rosemary. Transfer the meat to a cutting board and thinly slice. Using a slotted spoon, transfer the vegetables to a platter. If desired, transfer the cooking juices to a saucepan and reduce slightly to make a sauce.