Heat the olive oil in a skillet over medium-high heat. Add the beef stew meat and cook until browned on all sides, about 5 minutes.
Transfer the browned beef to the slow cooker. Add the diced onion, quartered mushrooms, minced garlic, and rosemary sprigs.
In a small bowl, whisk together the beef broth, tomato paste, salt, pepper, and flour until smooth. Pour this mixture over the ingredients in the slow cooker.
Cover and cook on low for 7 to 8 hours, until the beef is fork-tender.
Remove the rosemary sprigs before serving.