Dry off the quarters with paper towels. Heat up a large Dutch oven over a medium flame. Melt 2 Tbl of bacon fat in the pan. Sear the chicken on both sides in the hot grease. De-grease the pan, if desired. Pour in the beef stock. Throw in the onions, garlic, lime juice, tomato paste and water. Sprinkle in the flour. Stir to combine. Throw in the chile d'arbol powder, cumin, and salt to taste. Stir. Add 6 drops of worchestershire sauce and generous sprinklings of Tabasco.
Slowly bring the contents of the pan to a boil, cut the heat to a slow simmer. Every 15 minutes add a quick dash of worchestershire, many dashes of Tabasco and a handful of Longhorn cheese. Braise the dish for 1 hour. Stir the pot and turn the chicken over - routinely - during the braising period.
Pour the contents of the pot out onto a large platter. Serve with warmed, tortillas and more Longhorn cheese. Rip the chicken from the bones and place the chicken and cheese into quartered tortillas.