Roast the beef back ribs: Preheat oven to 475°F. Season rack of ribs lightly with kosher salt. Roast on a sheet tray for 12-15 minutes at 475℉, then turn oven up to broil and cook an additional 5-10 minutes to achieve deep caramelization. Remove and set aside.
Prepare two large pots: While the ribs are cooking, prepare two large pots on the stovetop. One pot will be for toasting the peppers and cooking the vegetables in beef stock, and the other (larger) pot will be for searing the chuck roast and stewing down the beef with the blended birria sauce.
Sear the chuck roast: While the ribs are roasting, cut the chuck roast into large chunks, about 2½ - 3". Season lightly with salt. Heat 2 tablespoons of beef tallow in the larger stock pot over medium-high heat. Working in batches, sear the chuck roast on all sides until deeply browned. Remove and set aside.
Prepare the dried chiles: Stem and seed all dried peppers. In a different dry pot over medium heat, toast the peppers for 2–3 minutes until fragrant. Do not let them burn. Remove and set aside.
Char the aromatics: In the same pot that you used to toast the peppers, add about 1 tablespoon beef tallow. Char the onion quarters over medium heat until softened and charred on the edges, about 5–8 minutes. During the last few minutes, add the garlic cloves.
Build and steep the chile sauce: To the pot with the onions and garlic, add the toasted chiles, cinnamon stick, bay leaves, peppercorns, all dried spices, roma tomatoes, and apple cider vinegar. Pour in the 4 cups of beef stock. Bring to a boil, then turn off the heat, cover and steep for 15–20 minutes until chiles are fully softened.
Blend and strain: Remove and discard the bay leaves and cinnamon stick. Blend the chile mixture until completely smooth, venting the blender lid carefully because the liquid is hot. Strain through a fine mesh strainer back into the pot, just to make sure there aren't any large chunks left.
Braise: Cut the beef back ribs into individual ribs. Place the seared chuck roast and the roasted beef back ribs in the larger stock pot. Pour in the blended chile sauce. Add water until the beef is just barely covered, about 2 cups depending on the size of your pot. Bring to a boil, then reduce to a low simmer. Braise for 2.5 to 3 hours, or until the chuck roast is completely pull-apart tender and the rib meat is falling off the bone.
Rest and shred: Remove all the beef from the pot and let rest for 10–15 minutes. Transfer all of the leftover sauce from the pot to a large bowl. Shred the chuck roast with two forks. Pull the rib meat off the bones and discard any silver skin. Combine all the shredded meat.
Skim the fat: Carefully skim the fat layer from the top of the sauce using a ladle or fat separator. Reserve this fat separately - it is pure concentrated beef flavor and is essential for dipping tortillas before frying for crispy tacos.
Season and finish: Taste the birria sauce and adjust salt as needed. Ladle some sauce over the shredded meat before serving to saturate it with flavor. Serve the sauce on the side for dipping, or ladle more over the beef in a bowl and serve as a stew.