Prep the mushrooms and save the mushroom soaking liquid:
Chop off the tough ends of the mushroom stems and either discard or save for stock. Roughly chop or slice the mushrooms and set aside. Dice the rehydrated porcini. Pour the porcini soaking water through a paper towel into another bowl. Reserve the liquid.
Dry sauté the mushrooms:
Heat a thick-bottomed large pot on high heat for 1 minute. Add the mushrooms and shake the pot. Stirring continuously, dry sauté the mushrooms until they release their water.
Turn the heat down to medium-high. Use a wooden spoon to scrape up any mushroom bits off the bottom of the pan. Salt the mushrooms lightly. When the mushroom liquid is mostly gone, remove them to a bowl.
Brown the rabbit in butter:
Add the butter to the pot. When the butter melts, turn the heat down to medium. Pat the rabbit pieces dry and place in the pan.
Work in batches if you need to, do not crowd the pan. Brown the pieces well on all sides. Remove the rabbit pieces from the pot and set aside.
Sauté the shallots:
Increase the heat to medium-high and add the shallots to the pot. Sauté until the shallots are nicely wilted, about 3 minutes. Stir from time to time. Sprinkle salt over everything.
Squeeze the garlic into the mushroom liquid:
While the shallots are cooking, squeeze the roasted garlic into the mushroom soaking water you have strained, then whisk it together.
Deglaze the shallots with sherry:
Add the sherry or white wine to the shallots in the pot. Use a wooden spoon to scrape off any browned bits on the bottom of the pot. Let the sherry boil down by half. Add the mushroom-roasted garlic mixture and the stock and stir to combine.
Add the thyme, mushrooms, rabbit, and parsnips, then bring to simmer and cook:
Add the thyme, all the mushrooms, the rabbit, and the parsnips and bring everything to a bare simmer.
Simmer gently for 90 minutes. You want the meat to be close to falling off the bone. If you want, you can fish out all the rabbit pieces and pull the meat off the bone – it makes the dish less attractive, but it will be easier to eat. Taste for salt right before you serve and add if needed. Stir in the parsley.
Serve:
Serve with a crusty loaf of bread, a green salad, and either a hearty white wine, a dry rose, or a light red wine.