Brown the beef: Heat olive oil in a large skillet over medium-high heat. Add the beef chunks in batches and sear until browned on all sides. Transfer to the slow cooker.
Add the vegetables: Place carrots, parsnips, potatoes, onion, and garlic into the slow cooker with the beef.
Build the base: Stir in diced tomatoes, beef broth, tomato paste, thyme, rosemary, bay leaves, salt, and pepper. Mix gently to combine.
Cook low and slow: Cover and cook on Low for 8 hours or High for 4 hours, until the beef is tender and vegetables are soft.
Add green beans: During the last 30 minutes of cooking, stir in the green beans.
Optional thickening: For a thicker stew, mix cornstarch with 2 tbsp water and stir into the stew 15 minutes before serving.
Serve and enjoy: Remove bay leaves, taste for seasoning, and serve hot with crusty bread or a side salad.