- Season rabbit quarters with salt and pepper liberally. Brown in hot pan to golden brown on all sides and remove from pan.
- Add carrots, celery, and leeks to the pan and sweat vegetables until soft.
- Deglaze with white wine and add currants, chicken stock, and duck fat.
- Season braising liquid with salt and pepper, add thyme and rabbit pieces, cover, and braise in 275-degree oven until fall-apart tender. Remove from oven. Let cool for 30 minutes in braising liquid.
- Shred the meat, discarding the bones. Mix in braising liquid and chill.
- Place in serving vessel (mason jar, bowl, etc.). Spoon melted duck fat or butter over the top just to cover. Let sit overnight.
- Serve on platter with grilled bread slices and relish or chutney as desired.