Heat a large cast-iron skillet over medium. Add chiles to skillet; cook, stirring occasionally, until fragrant, 4 to 5 minutes. Transfer chiles to a large saucepan; add onion, garlic, ginger, and 6 cups water. Bring to a boil over medium-high. Cook, uncovered, stirring occasionally, until chiles are softened, about 8 minutes. Drain chile mixture; discard cooking liquid.

Combine chile mixture, vinegar, salt, black pepper, oregano, cumin, cinnamon, cloves, thyme, bay leaves, and remaining 2 cups water in a blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, about 45 seconds. Let cool to room temperature, about 1 hour. Cover and chill until ready to use.

Gather the ingredients.

Sprinkle chuck roast and short ribs all over with 2 tablespoons salt. Combine roast, ribs, and adobo in a large nonreactive bowl; toss to coat. Cover and chill at least 4 hours or up to 24 hours.

Preheat oven to 300°F. Transfer adobo mixture to a large (9 ½-quart) Dutch oven; add 8 cups water. Bring to a simmer, uncovered, over medium, stirring occasionally.

Cover with lid and place in preheated oven. Bake until meat is fork-tender, about 4 hours.

Remove chuck roast and short ribs from braising broth and transfer to a large bowl; cover with aluminum foil to keep warm.

Return broth in Dutch oven to heat over medium and cook, uncovered, skimming off fat as needed, until reduced to about 8 cups, 15 to 20 minutes. Season broth with salt to taste.

Shred meat; discard bones.

Toss meat with 1 ½ cups of the broth.

Stir together onion, cilantro, and remaining ¼ teaspoon salt in a small bowl; set aside.

Heat a large nonstick electric griddle to 400°F or a large (12-inch) cast-iron skillet over medium-high. Using a paper towel dipped in canola oil, lightly grease griddle. If using fresh tortillas, stack two tortillas, and use tongs to dip them together into adobo broth. (If using packaged tortillas, dip one tortilla per taco.)

Place stacked tortillas on griddle; top with ¼ cup meat. Repeat with as many tortilla stacks as will comfortably fit on griddle. Cook until bottom tortilla is lightly browned and crispy, 1 to 2 minutes.

Fold tacos in half, gently pressing with a spatula. Transfer to a serving plate. Repeat process with oil, adobo broth, remaining tortillas, and remaining meat.

Serve tacos hot with onion-cilantro mixture, lime wedges, and remaining adobo broth for dipping or sipping.