Argentina is a meat lovers' paradise. In the farms and field villages of the central states the cooks love to braise with red wine, and rabbit is very popular there. This recipe is a favorite of Andrew Zimmern, host of the TV show Bizarre Foods.
Combine all Chimichurri Sauce ingredients except the oil and vinegar in a large mortar/pestle. Add the liquids once the herbs and seasonings are well pureed. Feel free to use a food processor if you must. Reserve.
In a large Dutch oven over medium-high heat, brown the rabbit pieces in the oil, in batches if need be. Remove and reserve rabbit, saute the vegetables and herbs until onions are glassy and add rabbit back to pot.
Add wine, bring to a slow boil and stir, then cover and cook, turning heat to low, for 90 minutes. Allow rabbit to cool in liquid with lid on for one hour at room temperature Then transfer rabbit to a work bowl, strain broth, pouring over the rabbit pieces and cover with plastic wrap, refrigerate.
Remove rabbit from wine broth, bring broth to a boil over medium heat and reduce to sauce consistency. Allow rabbit to come to room temp while sauce is reducing, and grill or broil to heat through and crisp the rabbit pieces. Serve rabbit, covering the meat with the sauce and passing lots of chimmichuri at the table.