Roasted potatoes and crusty bread, for serving
For the marinade: In a large deep tray or pan, place the bull's tails or oxtails in a single layer, standing upright. Press a couple of saffron threads into the top of each tail. Add the chopped vegetables to the marinade and pour in 1 bottle of Spanish red wine, or more if needed; the red wine should just cover all the ingredients. Leave to marinate in the refrigerator for 24 hours.
For the stew: Remove the bull's tails or oxtails and set aside. Strain the vegetables from the marinade and reserve both the liquid and the strained vegetables.
In a Dutch oven or deep, heavy skillet, heat the olive oil over medium-high heat. Add the fat, if using, and render down, 2 to 3 minutes. Add the reserved strained vegetables and saute until lightly caramelized, about 10 minutes. Add the bell peppers and continue to slowly caramelize all the ingredients together for 15 minutes longer.
Add the tails one by one, standing them upright and moving aside the caramelized vegetables underneath, so that the tails have direct contact with the bottom of the pan. When the underside of the tails has turned a gray color, 2 to 3 minutes, turn them over and repeat on the other side for an additional 2 to 3 minutes. Add in the reserved marinade. The liquid should just barely cover the bull's tails or oxtails. If needed, top up the liquid with water. Add the tomato concentrate or paste and demi-glace, if using.
Cook over slow, low heat until the meat from the tails is falling off the bone but still succulent and moist, about 4 hours. Check and correct the seasoning of the stew with salt and pepper.
Serve the stew immediately, garnished with finely chopped parsley, accompanied by roasted potatoes and crusty bread. This stew can also be made a day ahead and reheated to serve the following day.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.