Place the parsnips, potatoes or sweet potatoes and the onions in the slow cooker. Coat the brisket with the Dijon mustard and salt and pepper. Place on top of the veggies.
Add the thyme and bay leaves, and pour the beer over the meat. Cover and cook on high for 5 hours. In the last 15 minutes of cooking, place the beans on top of the meal. Cover again and cook on high until the beans are tender.
Remove the meat and the steamed beans from the slow cooker and set aside. Using two forks, shred (pull) the brisket. Drain the sauce from the slow cooker and set aside.
Add the butter to the veggies in the slow cooker with salt and pepper. Use a potato masher to mash the veggies until smooth.
Serve the meat with the mash and steamed string beans. Drizzle the remaining sauce over the top.