Step 1

Season the chuck roast and short ribs with salt and pepper. Set aside.

Step 2

Bring a pot of water to a boil and remove from the heat.

Step 3

Soak the guajillo and ancho chilis for 10 minutes.

Step 4

Remove the peppers from the water. Cut off the stem and remove the seeds.

Step 5

Put the peppers into the pitcher of a blender. Add one chipotle pepper, all of the adobo sauce, apple cider vinegar, tomato paste, garlic, oregano, paprika, cumin and cayenne.

Step 6

Blend the marinade until smooth.

Step 7

Place the meat in a large container and cover with the marinade. Toss to coat. Cover and marinade for 4 hours or overnight.

Step 8

Preheat oven to 300˚F.

Step 9

Heat the olive oil to a large dutch oven over medium heat.

Step 10

Add the onions and cook until softened.

Step 11

Transfer the meat and all of the marinade to the pot.

Step 12

Stir in the cinnamon sticks, cloves and beef stock.

Step 13

Cover and transfer to the oven. Braise the meat for 3 hours.

Step 14

Remove the Birria stew from the oven and skim off some of the fat. Reserve the fat to cook the tacos.

Step 15

With a slotted spoon, remove the stew meat to a platter and shred with two forks.

Step 16

Return the meat to the pot and stir to combine.

Step 17

Add one tablespoon of the reserved fat to a large skillet and heat over medium high heat.

Step 18

Dip the tortillas in the stew and add the tortillas to the heated skillet. (You may have to work one at a time depending on how big your skillet is.)

Step 19

Immediately top the tortilla with the shredded Oaxaca cheese. When the cheese has melted, add some of the shredded beef and fold one side of the tortilla over the other. Fry until crisp.

Step 20

Using a spatula, transfer the taco to a platter and keep warm.

Step 21

Repeat with the remaining tortillas. (You will have leftover Birria meat. Save for another dinner.)

Step 22

Top the finished Birria Tacos with chopped onion, queso Fresco, or cilantro, if desired.

Step 23

Serve with some of the stew broth for dipping!