Season the beef pieces with salt and pepper, then toss them in a bowl with the flour until evenly coated.
Heat the olive oil in a large skillet over medium-high heat. Add the beef in batches and brown on all sides, about 4 minutes per batch. Transfer the browned beef to the slow cooker.
Add the diced onion, carrots, turnips, minced garlic, and chopped rosemary to the slow cooker.
Pour the beef broth over the ingredients and stir gently to combine everything.
Cover and cook on low for 8 hours until the beef is fork-tender and the gravy has thickened from the flour coating.
Taste and adjust salt and pepper before serving.