Take the hare from the marinade and pat it dry.
Strain the marinade through a fine-meshed sieve into a bowl. Set aside the veggies.
Pour the marinade into a pot and bring to a boil. A raft of scum will form on top. Skim it off carefully. Bring the heat to a simmer, and skim the liquid several times until it is clear, then turn off the heat.
Heat half the goose fat or lard in a large pot or Dutch oven over medium-high heat.
Dust the pieces of hare in the rye flour — using something other than white flour adds a subtle earthy note to the civet — and brown them in the pot. Take your time with this; you may need to do it in batches. Once the hare is nicely browned, set it aside.
Meanwhile (you need to multi-task here), heat another tablespoon or two of the goose fat or lard in a large frying pan over medium-high heat. When it is good and hot, turn the heat down to medium-low and add the pancetta. If you are using bacon, only use enough goose fat to lubricate the bottom of the pan, as the bacon should be fatty enough.
Preheat the oven to 300 degrees.
Slowly cook the pancetta or bacon until crispy. Remove and set aside.
Add the veggies to the frying pan you cooked the pancetta in, and turn the heat all the way up. It will sputter. Toss and cook the veggies, adding more goose fat or lard as needed. Once they are coated and much of the liquid has steamed off, turn the heat down to medium and cook until they caramelize, about 10-12 minutes. Stir occasionally.
Return the hare to the Dutch oven and add the pancetta or bacon. Pour over the wine-brandy mixture, then add the veggies. Add the dried chanterelles, the quatre epices and the sugar. Make sure everything is evenly distributed.
If you think you need more liquid, add the game, veggie or beef stock. Bring this to a simmer and taste for salt — add some if needed.
Cover and put in the oven and leave it undisturbed for 2 1/2 to 3 hours for a hare, 90 minutes for rabbits.