Coat the rabbit pieces in seasoned ﬂour. Heat two-thirds of the butter in a large saucepan, add the rabbit and fry for 5 minutes, or until evenly browned. Remove the rabbit pieces from the pan and set aside.
Add the onion, carrot, swede and celery to the pan and fry together for 5 minutes. Then add the chopped mushrooms and cook them for 1 minute more. Return the rabbit pieces to the saucepan.
Stir in the water, add the bouquet garni and black peppercorns and bring to the boil. Reduce the heat, cover and simmer for 1 1/2–2 hours, or until the meat is very tender and comes away easily from the bone.
Remove the rabbit pieces from the saucepan, cool slightly, then strip the meat from the bones. Shred half of the meat and reserve. Remove and discard the bouquet garni. Purée the soup and the remaining meat in a food processor or blender.
Pour the soup back into the saucepan, add the reserved shredded rabbit meat and reheat. Stir in the port and season the soup to taste with salt.
Melt the remaining butter in a small frying pan and cook the sliced mushrooms until they are lightly browned.
Serve the rabbit soup piping hot, garnished with the fried, sliced mushrooms and the chopped fresh parsley.