Toast the ancho and guajillo chiles in a dry skillet over medium heat for 30 seconds per side until they turn slightly darker and release a toasty aroma. Transfer to a bowl, cover with just-boiled water, and soak for 15 minutes until softened.

Char the halved onion and Roma tomatoes directly over a gas flame or under a broiler set to high for 4 to 5 minutes, turning occasionally, until dark patches form on the surface.

Drain the soaked chiles and add them to a blender along with the charred tomatoes, charred onion half, garlic cloves, cumin, oregano, cinnamon, apple cider vinegar, and 250 ml of the beef stock. Blend on high for 60 seconds until completely smooth.

Pour the blended sauce through a fine-mesh sieve into a medium saucepan, pressing the solids with a spoon to extract as much liquid as possible. Discard the solids.

Add the remaining 500 ml beef stock, bay leaves, salt, and black pepper to the saucepan. Bring to a gentle simmer over medium heat.

Add the shredded smoked brisket to the simmering consomé. Stir to coat the meat, then reduce heat to low and simmer uncovered for 20 minutes until the fat from the brisket has rendered into the broth and the flavors have melded. Remove bay leaves.

Skim the red-tinted fat from the surface into a small bowl. Keep the consomé at a low simmer for dipping. Keep the brisket in the pot on the lowest heat setting.

Heat a 10-inch cast iron skillet over medium-high heat until hot, about 2 minutes.

Using a pastry brush or spoon, coat one side of a corn tortilla lightly with the skimmed consomé fat. Lay it fat-side down in the hot skillet.

Immediately layer a generous portion of Oaxacan cheese strips over one half of the tortilla, then spoon 3 to 4 tablespoons of drained brisket filling on top of the cheese.

Fold the empty half of the tortilla over the filling and press firmly with a spatula for 60 seconds until the cheese starts to bond with the tortilla surface.

Cook for 2 to 3 minutes until the bottom is deep brick-red and crispy. Flip carefully and cook the other side for another 2 minutes until equally crispy.

Transfer to a cutting board and repeat with remaining tortillas. Work in batches of two if your skillet is wide enough.

Ladle the hot consomé into small bowls, stirring in a pinch of diced raw white onion and cilantro.

Cut each quesadilla in half and plate alongside the consomé bowls with lime wedges. Dip each piece into the consomé before eating.