Prep the chiles. Remove stems and seeds from guajillo, ancho, and pasilla chiles.
Toast them in a dry skillet over medium heat for 30–45 seconds per side until fragrant. Don’t burn them.
Soften the chiles. Add toasted chiles to a bowl and cover with hot water. Soak for 15–20 minutes until pliable.
Reserve some soaking liquid.
Char the aromatics. In the same skillet, add halved onion and whole garlic cloves (peels on) and cook until lightly charred, about 5–7 minutes. If using fresh tomatoes, char those too. Peel garlic after charring.
Blend the sauce. In a blender, combine softened chiles, charred onion, peeled garlic, tomatoes, cumin, oregano, coriander, smoked paprika, vinegar, and 1 cup of broth.
Blend until very smooth, adding more broth or a splash of chile soaking liquid as needed. You want a thick but pourable sauce.
Season the beef. Pat the beef dry. Season all over with salt and pepper.
Optional: Sear the beef in a hot skillet with a little oil until browned on all sides for deeper flavor.
Load the slow cooker. Place beef in the slow cooker. Pour the blended sauce over it. Add bay leaves, whole cloves, and cinnamon stick.
Pour in enough broth to almost cover the meat.
Cook low and slow. Cook on Low for 8–9 hours or on High for 4–5 hours, until the beef is very tender and shreds easily.
Shred and skim. Remove beef and shred with two forks. Skim excess fat from the top of the cooking liquid, but keep some—it’s flavor and helps crisp tortillas. Taste the consomé and adjust salt.
Prepare for tacos. Warm a skillet or griddle over medium heat.
Lightly oil the surface with a mix of neutral oil and a spoonful of the birria fat from the consomé.
Dip and crisp. Dip a corn tortilla into the top layer of the consomé to coat lightly. Place on the hot skillet. Add a small handful of cheese and some shredded beef to one side.
Fold and cook. Fold the tortilla over the filling.
Cook 1–2 minutes per side until crispy and the cheese melts. Repeat with remaining tortillas.
Serve with consomé. Ladle hot consomé into small bowls for dipping. Top tacos with chopped onion, cilantro, and a squeeze of lime.
Serve immediately.