Quesabirria

Place pork shoulder chunks in a large pot and cover with vegetable broth. Add quartered onion and smashed garlic. Bring to a boil, then reduce heat and simmer for 2 hours until meat is very tender.

Remove meat from broth and shred using two forks; set aside. Strain broth through a fine-mesh sieve into a clean pot, discarding solids.

Toast dried chiles in a dry skillet over medium heat for 1 minute until fragrant. Soak in 1 cup hot water for 15 minutes, then blend with the soaking liquid until smooth.

Add blended chiles, tomato paste, apple cider vinegar, cumin, and oregano to the strained broth. Simmer for 15 minutes. Season with salt and black pepper to taste.

Heat vegetable oil in a shallow skillet over medium-high heat until shimmering.

Place one flour tortilla on a work surface. Dip the bottom side briefly into the hot consomé, then lay it wet-side down in the skillet. Quickly add a small handful of shredded cheese and 2 tablespoons shredded meat to one half.

Fold the tortilla in half and press gently with tongs until golden and crispy on the first side, about 2 minutes. Flip and cook the second side until golden, another 1–2 minutes. Transfer to a plate lined with paper towels.

Repeat with remaining tortillas, cheese, and meat, adjusting heat as needed to maintain a steady sizzle.

Arrange quesadillas on a serving platter. Pour warm consomé into individual dipping bowls. Garnish with diced white onion and fresh cilantro. Serve with lime wedges on the side.