Cooking the Meat
Season the roast liberally with all of the seasonings. Ensure that it is rubbed into the beef until coated evenly. Place the meat in the slow cooker, or in a large dutch oven.
Cover with water, add the beef bouillon cubes and chopped onion. If using a slow cooker, place the heat to high and cook for 4-5 hours. If placed on low heat, cook for 6-8 hours. For dutch oven, cover and place in the oven at 350 degrees for 4-5 hours.
Preparing the Consomé
Cut or tear the guallijo and ancho peppers down the middle to remove and discard the seeds and stems.
Place the chiles, tomatoes, cloves, bay leaves, and all of the other seasonings and spices into a stockpot and cover with about 3-4 cups of water. Bring the mixture to a rapid boil for 10 minutes. Remove the pot from the heat and allow it to cool to room temperature.
Using tongs or a fines strainer, carefully remove the bay leaves and cloves from the water mixture (save the water to use later). Add the peppers (and tomatoes if they didn’t dissolve), into a blender with about 1 cup of the cooking water.
Blend on high for 1-2 minutes, or until the mixture is completely pulverized. Using a fine mesh strainer, strain the chile mixture into another stockpot by pushing it around the strainer with a spoon. Add a little bit at a time, until all of the chile mixture is used.
Use liquid the chiles were boiled in, and liquid the beef cooked in to pour into the fine mesh strainer (a little at a time), and continue pushing it through with a spoon. This is to ensure all of the flavors are extracted from the chile mixture.
Squeeze the lime juice into the consomé mixture, and heat over medium on the stove top while preparing the birria queso tacos.
Birria Queso Tacos
Pour 1/2 cup of the consomé onto a shallow plate or dish. Add 2 tablespoons of vegetable oil to a large skillet over medium heat.
Dip one corn tortilla at a time into the consomé, then place it flat into the oil in the skillet. Add about 1-2 tablespoons of beef, and shredded cheese onto one side of the tortilla.
Fold the other side over to form a taco shape. Fry each side of the taco for 2-3 minutes, until both sides are golden brown and crispy.
Remove and place on a paper towel of baking rack to drain excess grease. Repeat this process until all of the tacos are made.
Serve with onion, cilantro, lime wedges, and some consomé to dip the tacos in.