Trim any excess fat off of the brisket, leaving about 1/4" of fat. Season it well on all sides.
Using a large cast-iron casserole dish, heat over medium heat and add the olive oil. Sear the brisket for 3-4 minutes on each side to lightly brown and generously season. Transfer the brisket to a clean surface.
Using the same pan, saute the carrots, and onions for 5-6 minutes or until lightly softened. Lightly season with salt and pepper and add the garlic. Saute for another 2 minutes. Push the vegetables to the edge of the pan, making space for the brisket.
Add the brisket to the pan and top with coconut sugar, tomato sauce, and parsley. Pour the broth and vinegar into the base of the pan, add the bay leaves and cover the pan.
Cover and transfer to the oven and roast for 2 hours. Reduce the oven heat to 300 F and roast for another 1 1/2 hours, checking halfway to ensure the brisket is not over cooking. It should be tender when done.
Remove the brisket from the oven and allow to rest before slicing and serving with the side of the vegetables, and topping with the cooking juices.
Notes
If you don't have a large casserole dish, you can sear the brisket in a pan and roast it in a covered baking dish or roasting pan.To make this brisket AIP, omit the black pepper and use nightshade-free tomato sauce. If using a whole brisket, add 30 minutes to the cook time as needed until the brisket is cooked through.All nutritional information are estimations and will vary. Estimations do not include optional ingredients.