Heat the olive oil in a large skillet over medium-high heat. Add the beef stew meat and brown it on all sides for about 5 minutes. Transfer the meat to the slow cooker.
Add the diced onion, minced garlic, carrots, potatoes, parsnip, and turnip to the slow cooker. Stir in the tomato paste, thyme, rosemary, salt, and black pepper.
Sprinkle the flour over the meat and vegetables, then pour in the beef broth. Stir everything to combine and coat the ingredients evenly.
Cover the slow cooker and cook on low for 8 hours or on high for 4 hours, until the beef is tender and the vegetables are soft.
Taste the stew and adjust salt or pepper if needed. Sprinkle the chopped fresh parsley over the top just before serving.