In a heavy bottomed sauté pan, heat the 2 tsp of tallow over medium heat. Saute the onion, leeks and garlic until browned. Remove to slow cooker.
Return the pan to the heat (medium) and add the second 2 tsp of tallow. Sear the rabbit pieces on all sides (you may have to do this in more than one turn). Season the rabbit with salt and pepper as you sear it. Remove the seared pieces to the slow cooker.
Deglaze the pan with the two cups of water, then whisk in the Dijon and Balsamic vinegar. Pour the sauce over the rabbit and onions in the slow cooker.
Toss the mushrooms into the slow cooker and top with the fresh herbs. Cover and cook on low for 6 hours or on high for 3 hours.
Serve with mashed potatoes, roasted root veggies or whatever strikes your fancy!