Place a large roasting pan over two burners and add 2 Tbsp. oil; heat over medium heat. Add the brisket and cook until browned, 8 to 10 minutes on each side. Transfer the brisket to a rimmed baking sheet.
Add the remaining 2 Tbsp. oil to the pan. Stir in the onions and garlic and season with a little salt. Cook over medium heat, stirring often, about 15 minutes, or until onions are a golden brown and soft. Stir in the paprika and cumin and cook for one minute more.
Add tomato puree and brown sugar; cook, stirring, for 5 minutes. Stir in coffee and chicken broth and bring to a simmer.
Return the brisket to the pan. Cover tightly with foil and transfer to a preheated 325-degree oven. Roast until the brisket pulls apart easily, about 3-1/2 to 4 hours.
Transfer brisket to a cutting board and let rest for 30 minutes. Skim fat from the braising liquid; season with salt and pepper. Slice the brisket against the grain 1/4 inch thick and return slices to the roasting pan. Place pan over two burners and warm the brisket over medium heat until heated through, about 10 minutes.
Serve with mashed potatoes; serve the braising liquid as gravy/broth.