Combine pork shoulder roast, garlic cloves, tomatoes, onion, guajillo chiles, cumin, salt, and pepper in a large (5 to 6-quart) slow cooker; pour chicken broth over roast.

Cover and cook on High until pork is fork tender, 6 to 7 hours. Remove roast from slow cooker; allow to cool for about 10 minutes. Shred pork with forks, discarding any fat or membranes.

Discard bay leaves. Pour cooked vegetables and liquid through a sieve; reserve cooking liquid. Place cooked vegetables in a blender or food processor; blend to smooth puree.

For dipping sauce, skim excess fat from cooking liquid; set fat aside. Return puréed vegetables and defatted cooking liquid to the slow cooker; cook, covered, on High.

Add a bit of reserved fat to a skillet over medium-low heat. Soften tortillas by warming on each side for 1 to 2 minutes.

To make tacos, place shredded cheese, shredded pork, and more shredded cheese on a warm tortilla. Fold and repeat for all tortillas.

Add a thin layer of reserved fat to the skillet over medium heat. Cook folded tacos until golden, 3 to 4 minutes per side.