If the rabbit has not been cut up, then break it down to 6 pieces. Use a heavy chef's knife or cleaver. Cut off both the hind legs. Separate the saddle, or back section, of the rabbit from the front two legs. Cut the saddle in half crosswise. Separate the two front legs.
Season the rabbit pieces on both sides with kosher salt and pepper. Heat a wide skillet over medium high heat. When the pan is hot, add the olive oil. Add the rabbit pieces to the hot skillet and sear undisturbed until well browned. The rabbit may stick to the pan initially, but it will release once it’s browned.
To make the braising liquid, turn the heat on the skillet down to medium and then add the shallots. Sauté the shallots until they are soft and translucent. Add the minced garlic to the skillet. Cook for another minute until the garlic is fragrant. Turn the heat back up to medium high and deglaze the pan with the wine.
Simmer the wine for a minute to reduce slightly. Add both the Dijon mustard and grainy mustard along with the chicken broth. Whisk together. Tie the parsley sprigs, thyme, and bay leaves together with wine and add to the braising liquid.
Return the rabbit pieces to the pan and turn the heat down to medium low. Cover and let gently simmer for 45 to 50 minutes until the rabbit is tender.
When the rabbit is fully cooked and tender, remove the pieces to a separate plate to finish the sauce. Remove the herb bundle. Bring to a boil and then add the heavy cream. Let simmer to reduce slightly. Taste and adjust the seasoning if necessary.
In a small cup, combine the water and cornstarch. Whisk the cornstarch slurry to the sauce. Simmer until the sauce has thickened. Stir in the chopped parsley and return the rabbit to the sauce. Garnish with more chopped parsley and enjoy!
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