Season the beef with 2 teaspoons of the salt and the ground black pepper.
In a 6-quart pressure cooker, add the guajillo chiles, the ancho chiles, 1/2 of the onion, the garlic cloves, the ginger, the tomatoes, and the water and stir to combine.
Using the "Sauté" option over high heat, bring the onion mixture to a boil, and cook, about 10 minutes.
Turn the pressure cooker off.
Use a slotted spoon to transfer the onion mixture to a blender, reserving the cooking liquid in the pressure cooker.
Add 2 cups of the cooking liquid, the remaining teaspoon of salt, the apple cider vinegar, the black peppercorns, the Mexican oregano, the cumin seeds, the ground cinnamon, and the ground cloves to the blender and blend on high speed until the mixture is smooth, about 1 minute.
Place a fine mesh strainer over a large bowl.
Pour the blended mixture through the strainer and use the bottom of a ladle to push the sauce through the strainer until a thick paste remains. Discard the thick paste.
Empty, wash, and dry the inside of the pressure cooker.
Add the oil to the pressure cooker and heat it on the "Sauté" setting over high, about 5 minutes.
Add the beef, in batches, and sear until it has browned on a few sides, about 8-10 minutes.
Transfer the beef to a large plate.
Return all the seared beef and its juices to the pressure cooker.
Add the strained sauce, the beef broth, and the thyme sprigs to the beef and stir to combine.
Lock the lid on the pressure cooker and ensure the valve is set to seal.
Set the pressure cooker to cook on "High Pressure" for 40 minutes. It will take about 15-20 minutes for it to come up to pressure.
Let the pressure release naturally, for about 15 minutes, then quick-release any of the remaining pressure.
Preheat the oven to 250 degrees F.
Line an 18x26-inch baking sheet with parchment paper.
Use a slotted spoon to transfer all of the cooked beef to a large bowl, then use two forks to shred the beef. Reserve the cooking liquid in the bowl and discard the fat and the thyme sprigs.
Season the beef with the extra salt and the pepper.
Heat a griddle or large nonstick frying pan over medium heat.
Dip the tortillas, one at a time, in the reserved cooking liquid and then place as many tortillas as will fit in a single layer on the griddle.
Sprinkle the tortillas with 1/4 cup of the cheese.
Top the cheese with 1/4 cup of the shredded beef.
Drizzle the shredded beef with some of the remaining cooking liquid.
Cook the tortillas until the cheese has melted and then fold each tortilla in half.
Flip the tortillas and cook until they are browned in spots and crispy, about 5-6 minutes
Place the tacos onto the prepared baking sheet and transfer it to the oven to keep them warm.
Repeat the process until all the remaining taco ingredients have been used.
Top the tacos with the onions, the cilantro, the lime wedges, and the remaining cooking liquid for dipping.
Serve.