In a large cast-iron skillet with heavy lid on medium-high heat, add the bacon. Cook until the bacon is crispy and remove to a paper towel and drain.
In the same pan on medium heat, add the onions, celery, bell pepper, and mushrooms to the remaining bacon grease. Sauté the ingredients just until the onions turn translucent and then add the carrots and garlic along with the parsley, rosemary, and kale. Stir all the vegetables together for 2 minutes and then remove to a platter.
Place the rabbit pieces on a platter and pat dry with paper towel. Season with salt and pepper. Dredge the pieces lightly in flour and place on a platter.
In the same pan on medium heat, add the oil. Once the oil is hot, add the rabbit pieces. Brown the rabbit on both sides.
Pour off any remaining oil from the pan and add the sautéed vegetables and the bacon pieces back to the pan with the rabbit. On medium heat, add the wine and deglaze the pan. Cook until the wine reduces by half. Add both mustards and stir until combined. Add 1 cup of chicken stock. Lower the heat to a simmer, place the cover on the pan and let cook for 20 minutes.
Uncover, add the cream and stir to combine. Cover and let simmer for 10 minutes. Stir to make sure the sauce is thickening, but not sticking on the bottom of the pan. Add more chicken stock to thin it out, if needed. Cover and simmer for another 10 minutes until the rabbit is tender. Taste the sauce and add salt and pepper as needed. Cover the pan and keep warm.
For serving, present the pan in the center of the table in traditional farmhouse style. Serve with steamed rice or mashed potatoes along with crusty French bread, and of course, a bottle of French Burgundy wine.
