1. Turn on and pre-warm your slow cooker. Pat dry your lamb with a paper towel then season with salt and pepper. Grease a large pot with butter or oil.
2. Place the lamb in the pot greased with butter or oil and fry until golden brown.
3. Using tongs, turn the lamb the other side. Make sure you brown from all sides. When brown, take off the heat and set aside.
4. Chop the mint and peel and slice the garlic. Place your lamb in the slow cooker and sprinkle garlic and mint over the lamb. If the lamb becomes dry, add 1/2 - 1 cup of water into your slow cooker with the lamb.
5. Place the lid on and cook on low for 7 hours in a slow cooker.
6. After 5 hours of cooking, transfer the lamb to a plate. Place the green beans into the slow cooker and re-add the lamb. Cook lamb and beans for another 1-2 hours until the green beans are crisp-tender and the meat is soft and juicy.