Preheat the oven to 350°F (180°C). Rub the lamb shanks with olive oil and salt and place in a large cast-iron pot. Sear for 30 minutes until golden brown. Lower the heat to 300°F (150°C) and add the root vegetables and beer to the pot, saving a little beer in case you need it later on.
Place the lamb shanks on top, cover and let braise for 2 ½ – 3 hours, or until the meat is giving, occasionally pouring cooking juice over the shanks. Make sure the pot doesn’t dry up – in case, add more beer as you go.
When the meat is done, set to one side and keep warm. Strain off the cooking juices, reduce and season if necessary, and keep warm. Make the puree by adding cream and butter to the root vegetables, crushing them together until you have a fine puree. Add salt and pepper to taste.