To make the mirepoix, rinse, trim, and peel celery, onion and carrots. Chop into uniform pieces and add to a pan with beef stock then season with salt and pepper to taste.
Blend together brewed coffee and ancho chili until it forms a liquid paste consistency. Season short ribs with coffee ancho paste on all sides, then put into a shallow baking pan with bottom of pan covered with mirepoix mix. Place into the oven to braise at 350°F for about 3.5 to 4 hours until tender then let rest until serving.