1 Sprinkle rabbit pieces with salt: Place rabbit pieces on a platter, sprinkle both sides with kosher salt. Let sit for 30 minutes to an hour.
2 Dredge rabbit with flour, brown in butter: Place flour on plate. Dredge rabbit pieces in flour.
Heat oil and butter in a large Dutch oven on medium heat (large enough to fit rabbit pieces in a single layer). Once the butter is melted and foamy, add the rabbit pieces in a single layer to the pot.
Brown on one side without stirring for 5 to 6 minutes. Then turn the pieces over and brown on the other side. Remove to a plate.
3 Brown the onions, add garlic and thyme: Add the sliced onions to the pot, and cook, stirring occasionally, until lightly brown, scraping up and browned rabbit bits from the bottom of the pot. Add garlic cloves and thyme, cook until onions are soft and the garlic quite fragrant.
4 Add ale, then stock, salt, pepper: Increase the heat to high and add the Belgian ale. Let it simmer for a minute or two, then add the stock. Add a half teaspoon of salt and the freshly ground black pepper.
5 Add celery root, rabbit, then simmer: Place the diced celery root over the onions in a single layer. Place the browned rabbit pieces over the celery root. Bring to a simmer. Cover and reduce heat to maintain a very low simmer. Cook for 45 minutes, or until the rabbit is just cooked through and tender.
6 Reduce sauce: Remove rabbit pieces from the pot and keep warm on a platter. Increase the heat to high and reduce the liquid by one third. Then, reduce the heat to low, stir in the mustard and sugar. Taste and add more salt and pepper in needed.
7 Return meat to sauce in pot: Slice the flap meat pieces of the rabbit into strips and return to the pot. Strip away any available meat from the back and chest parts and return meat to the pot. Add the serving pieces to the pot. Cover and let rewarm for a minute.
8 Serve: Sprinkle with chopped parsley to serve. Serve with crusty bread, egg noodles, or rice pilaf, along with some Belgian ale.