Carefully cut open each dried chili pepper to remove the seeds. Toast the chiles in a large skillet set over medium heat until fragrant (1-2 minutes), then place them in a pot filled with simmering water for 15-30 minutes or until the chiles are rehydrated and softened. Save the chili liquid.
In the same skillet, brown the onions in one tablespoon of olive oil for 1-2 minutes. Add the garlic cloves and sauté for 30-60 seconds or until fragrant. Remove everything to a clean plate and set aside. With the skillet still set over medium-high heat, add the tomatoes and cook each side for approximately 1-2 minutes. Remove the tomatoes to a clean plate.
Add a final tablespoon of olive oil to the skillet. Toast the cumin seeds, black peppercorns, whole cloves, and cinnamon stick for 1-2 minutes or until fragrant.
Return the onions, garlic, and tomatoes to the skillet and add the ground ginger, thyme, oregano, and marjoram. Mix well to combine, then remove from heat.
Transfer the onions, tomatoes, and all the spices to a high-speed blender, plus the rehydrated chilies and 1-2 cups of the soaking liquid. Blend until smooth.
Transfer the chili sauce to a large pot or Dutch oven set over medium-high heat. Add the orange juice, apple cider vinegar, beef, and bay leaves. Bring it to a simmer, then cover it with a lid, reduce heat to low, and cook for at least 3-4 hours.
Remove the beef from the pot and shred it with a fork. Save the birria broth (consummé).