Preheat the oven to 325 degrees . Place a large roasting pan over two burners. Add 2 tbsp. oil and heat over medium. When the oil shimmers, add the brisket and cook until browned, 8 to 10 minutes per side. Transfer the brisket to a rimmed baking sheet.
Add the remaining 2 tbsp. oil to the pan. Add the onions and garlic and season with salt. Cook over medium heat, stirring often, until the onions are golden-brown and soft, about 15 minutes. Stir in the paprika and cumin and cook for 1 minute. Add the tomato puree and brown sugar and cook, stirring, for 5 minutes. Stir in the coffee, chicken broth and cardamom pods and bring to a simmer.
Return the brisket to the pan. Cover snugly with foil and transfer to the oven. Roast until the brisket pulls apart easily, 3 1/2 to 4 hours.
Transfer the brisket to a cutting board and let cool for 30 minutes. Skim any fat from the braising liquid; season with salt and pepper. Slice the brisket against the grain 1/4 inch thick and return to the roasting pan. Place the roasting pan over two burners. Warm the brisket over medium until heated through, about 10 minutes.