Heat a large pan to medium heat and add the dried peppers. Dry toast them in the hot pan 1-2 minutes per side, until the skins darken.
Remove from heat and add the toasted peppers to a large bowl. Cover with hot water and steep 20 minutes, or until softened.
While the peppers are rehydrating, heat the olive oil in the same pan to medium heat.
Add the onion and tomatoes and cook for 5 minutes to soften.
Add the garlic and cook another 1 minute, stirring.
Add the cooked onion, tomatoes and garlic to a food processor.
Remove the softened chilies and add to the food processor, but reserve the soaking liquid.
Add the seasonings to the food processor along with the vinegar and 1 cup beef stock. Process until smooth. It should be fairly thick. You can strain if you’d like for a smoother sauce. See the RECIPE NOTES below.
Cut the lamb (or beef) into large chunks and add to a large bowl.
Pour the birria sauce over them and rub it into the meat. Cover and marinate the meat in the refrigerator for 2 hours minimum. Overnight is better.
Optional: Sear the Meat. For extra depth of flavor, remove the meat from the marinade and pat it dry (reserve the marinade for later). Heat a drizzle of oil in your Dutch oven or large pot over medium-high heat. Working in batches, sear the meat on all sides until browned, 2-3 minutes per side.
When you’re ready to cook, add the meat with all of the marinade, the chopped roasted tomatoes and remaining 3 cups beef broth to the large pot. Cover and cook at medium heat for 3 hours, or until the meat is fork tender and easy to shred. Add more beef stock or some of the reserved soaking liquid if needed for a soupier birria.
Serve the braised birria into bowls as a soup, or shred the meat and serve it up onto tortillas as birria tacos, with the reserved liquid consome from the pot as a side soup/broth.