Preheat oven to 180°c-350°f.
Heat the olive oil in a large pot over medium-high heat. Once hot, add in the lamb shanks and sear until golden all over, turning frequently. Transfer to a plate.
In the same pan, add in the onion, garlic, carrots, potato and celery, saute for 5 minutes, stirring frequently. Add in the tomato paste, red wine, chicken stock, thyme, whole fennel seeds, whole cumin seeds, oregano, bay leaves & place the lamb shanks back in, including any juices that have accumulated on the plate. Mix well.
Bring to a boil, place on a lid and transfer the pot to the oven. Braise for 3 ½ hours. Carefully remove from the oven.
Transfer the lamb shanks to a plate. Gently strain & scoop out the vegetables. Pour the sauce into a saucepan and leave the vegetables in the original pot to keep hot.
Place the saucepan onto the stovetop over high heat & bring to a boil. Reduce heat to medium-low and simmer for 25 minutes or until well reduced and thick.
In the meantime, place a pan onto the stovetop over medium-high heat. Add in the snake or green beans. Pour in the hot water and simmer until the beans start to soften and the water is nearly evaporated. Add in the unsalted butter and seasoning to taste. Saute for 1-2 minutes or until cooked through and buttery.
Serve the lamb shanks on top of the beans, serve with the lamb vegetables and top with the amazing lamb sauce reduction.