Place the beef in a large pot with the onion, garlic cloves, and salt. Cover with plenty of water and cook using your preferred method (stovetop, slow cooker, or pressure cooker) until the meat is tender. Once cooked, transfer the beef to a bowl and shred it using two forks. Set aside.

In a large bowl, combine the sliced cabbage, onion, carrots, and jalapeño peppers. Add the lime juice, white vinegar, oregano, and salt. Mix well to evenly distribute the seasonings. Set the salad aside to allow the flavors to meld.

In a small saucepan, combine the pasilla chilies and tomatoes, then cover with water. Bring to a simmer over medium heat and cook until the chilies and tomatoes are softened, approximately 10 minutes. Remove from heat and allow to cool slightly. Transfer the chilies, tomatoes, and 2 cups of the cooking water to a blender. Add garlic and salt, blending until the mixture is smooth. In a separate saucepan, heat the lard or oil over medium heat, then add the blended sauce. Allow it to simmer for approximately 10 minutes or until it thickens slightly. Adjust the salt to taste and set aside.

Place the masa harina in a mixing bowl. Gradually add the lukewarm water, kneading until a smooth and non-sticky dough forms. Divide the dough into 12 equal portions, shaping each into a small ball. Cover the dough balls with a damp kitchen towel to prevent drying. Place a dough ball between two sheets of plastic and use your hands or a rolling pin to press it into a disc approximately 3.5 inches (9 cm) in diameter. Carefully peel away the plastic and place the disc onto a preheated cast-iron skillet or comal set to medium-low heat. Cook for 1 to 1.5 minutes on one side, then flip and continue cooking for an additional 3 to 4 minutes, flipping once or twice until dark spots form. Transfer each cooked masa cake to a plate lined with a kitchen towel, and repeat until all dough is used.

In a large pan, heat about 3 to 4 tablespoons of lard or frying oil over medium heat. Place a portion of shredded beef on each masa cake, then carefully add them to the pan to fry. Top each garnacha with a spoonful of salsa, followed by 1 to 2 tablespoons of the cooking oil to allow the meat and salsa to slightly fry on top. Fry until the bottom of the garnachas is crispy and golden. Once ready, transfer the garnachas to a serving plate.

Top each garnacha with chopped onion and a sprinkle of Cotija cheese. Serve alongside the cabbage salad for a complete meal.