Preheat oven to 300°F.
Remove brisket from package and dry with paper towels.
Coat each side of brisket with dry rub.
Preheat Dutch oven on medium heat, and add oil. Once oil is hot, sear brisket for 2 minutes per side.
Remove brisket and set aside, while keeping the Dutch oven on the heat. Add onions, carrots and garlic, sauté for 3 minutes. Add the thyme and cinnamon sticks, sauté for 3 more minutes.
Deglaze Dutch oven with madeira and let it reduce by half.
Add beef stock, and bring to a simmer. Once liquid is simmering, place brisket back in Dutch oven, cover and place in oven. Cook for 4 hours or until brisket is fork-tender. Remove brisket and set aside to rest.
To make the madeira sauce, remove thyme and cinnamon sticks, then pour everything into a blender - yes, carrots and onions as well this will thicken the sauce and give more flavor. Blend for 2 minutes.