Place the beef cubes in a bowl and toss with the flour, salt, and black pepper until evenly coated.
Heat the olive oil in a skillet over medium-high heat. Add the beef and cook for 4 to 5 minutes, turning to brown on all sides.
Transfer the browned beef to the slow cooker. Add the diced onion, sliced carrots, and minced garlic.
Stir in the crushed tomatoes, tomato paste, beef broth, and Italian seasoning. Add the rosemary sprigs on top.
Cover and cook on low for 8 hours or on high for 4 to 5 hours, until the beef is fork-tender.
Remove and discard the rosemary sprigs before serving. Stir the stew to check that the gravy has thickened from the flour and tomatoes.