Preheat oven to 325 degrees F.
Combine 2 tablespoons olive oil with garlic cloves, shallots, rosemary, thyme, anchovies, salt, and pepper in a food processor. Pulse ingredients until they turn into a paste. Rub paste onto brisket, making sure to cover all sides. Let sit for 30 minutes.
Heat 1 tablespoon oil in a large Dutch oven over medium heat. Lightly sear brisket on all sides, lightly caramelizing rub onto the meat. Remove and set aside.
In the same pot, heat another tablespoon oil. Add chopped onion and carrots and cover the pot. Continue to cook for 3 minutes or until vegetables are beginning to soften. Remove lid and add tomato paste, stirring to coat. Add wine and bring to a boil. Continue to boil for 1 minute.
Add back brisket to pot along with beef broth, balsamic vinegar, worcestershire, and lay leaf. Bring to a simmer and cover the pot. Continue cooking in the oven for 2 ½ hours or until beef falls apart easily.
Meanwhile, make gremolata. Combine chopped parsley with olive oil, almonds, capers, lemon juice and zest, and garlic in a medium bowl. Season with salt and pepper and let sit for at least 30 minutes.
Remove brisket from the oven and spoon gremolata on top. Serve with additional gremolata on the side.