Start by removing the stems and seeds of ancho and guajilo chilies, as well as chilies de arbol.
Season all the meat generously with salt. In a large oiled pot heated over medium heat, add the meat in batches and sear 2-3 minutes on all sides. Once seared, take out the meat and leave on the side.
Add a bit more oil to the pot back on medium heat and add chopped onions. Saute until just softened.
Once softened, add tomato paste and cook down until paste starts to darken.
At which point, add sliced garlic and saute until fragrant and add rich beef stock. Mix together and add in chilies.
Add the meat back in.
Separately in cheesecloth, add black pepper corns, toasted coriander, cinnamon stick, and bay leaves. Fold together and tie tightly.
Toss the spice bag mixture into the stock and bring to a light simmer and cover. Braise for 1 hour stirring occasionally.
After 1 hour, remove the chilies and place into a blender with a little of stock liquid and blend until smooth.
Pour back into the stew and bring back to a simmer. Cover and braise for 90 minutes.
Remove the meat (and any bones) and shred using a fork.
Season the rest of the broth with salt and place to the side.