Wash the lamb stilt, dab dry and rub with salt and pepper. Heat the oil in a roaster. Fry the stilts in it all around. Place the roaster in the preheated oven (electric range: 175 °C/ gas: level 2), pour on some stock and braise for 45 minutes.
In between, gradually pour on the remaining stock and wine. Clean and wash the Brussels sprouts and possibly halve them. Peel, wash and cut carrots and potatoes into pieces. Add the vegetables to the stilts and cook for another 45 minutes.
Season vegetables with salt, pepper and dried thyme. Garnish with parsley and bay leaves to taste before serving.