Preheat oven to 300°F or preheat slow cooker to low.
Heat a large sauté pan or Dutch oven, lightly coated with evoo, over medium-high heat. Brown onions until dark and very soft. Stir tomato paste in and continue cooking for a few minutes to sear tomato paste. Transfer onions to slow cooker, or if using a Dutch oven, push onions to the side.
Season brisket with salt and pepper and brown on both sides in the same pan. You may need to cut brisket in half to fit into a slow cooker.
Nestle brisket into pan with onions. Add garlic, broth, wine, and bouquet garni.
Cover and braise for 3½ to 4 hours in a 300°F oven or 8 hours on slow cooker, or until a fork inserted, comes out with no resistance.
Cool brisket before refrigerating for up to 2 days.
Scrape off fat, slice brisket. Squeeze garlic out of heads and add to pan juices. Serve with pan juices and onions.
Slice brisket if serving another day and store with pan juices in refrigerator. Reheat in a 300°F oven, covered, for 1 hour.