Slice the stems off the guajillo, ancho, and arbol chilies, deseed them, and rinse under cool water to remove any dust. Place all chilies in a medium pot, cover completely with water, and bring to a simmer over medium heat. Simmer for 15 minutes, until the chilies have softened.
While the chilies are simmering, arrange the Roma tomatoes, quartered white onion, and unpeeled garlic cloves on a sheet pan. Broil them in the oven for 4 to 6 minutes, turning as needed, until lightly charred. I find that charring the vegetables adds a wonderful smoky depth to the sauce.
Transfer the softened chilies and 1 cup of the chili simmering water to a high-powered blender. Peel the roasted garlic and add it to the blender along with the charred tomatoes and onion from Step 2. Add the beef broth, apple cider vinegar, kosher salt, black pepper, ground cumin, Mexican oregano, ground cloves, ground cinnamon, and ground ginger. Blend on high for 1 to 2 minutes, until you have a completely smooth sauce.
Place the beef chuck pieces into the slow cooker. Pour the blended birria sauce over the beef, add the bay leaves, and use tongs to gently mix everything together. Cover and cook on low for 8 to 9 hours or on high for 4 to 5 hours until the beef is tender and shreds easily. If the beef doesn't shred easily, let it cook a bit longer. I recommend starting it early—the longer it cooks, the richer the flavor will be.
Once the beef is done, discard the bay leaves. Transfer the beef to a cutting board and shred using two forks. Return the shredded beef to the slow cooker and stir to combine with the sauce, letting it soak up the flavorful consommé.
Serve the birria directly from the slow cooker in bowls with consommé for a traditional birria stew, or use it for tacos, quesadillas, or other dishes. Garnish with diced onion, chopped fresh cilantro, and a squeeze of lime juice. For extra brightness, I love to serve mine with plenty of lime wedges.