Rub the beef roast with salt, pepper, chipotle powder, smoked paprika, and crushed garlic and a touch of oil. Cover the roast with plastic wrap. Let the meat marinate in the refrigerator for 2-4 hours or overnight.
Heat 1 tablespoon of cooking oil in a cast iron skillet over medium-high heat. Transfer the roast to the skillet and sear on all sides. If you're using a pressure cooker, use the sauté function for this step. Once the roast is charred on all sides, slice it into 4 pieces.
Deglaze the skillet with splash of beef broth over a medium flame and use a whisk or wooden spoon to loosen the bits left behind from the roast. Once the liquid simmers and most of the bits are released, cut the flame and proceed to the next step.
Place the roast in a dutch oven or pressure-cooker pot and pour the deglaze liquid over it. Add the quartered onions, tomatoes, cinnamon stick, bay leaves and chili peppers. Bring the pot to a boil, then cover and turn the flame down low. Let simmer for 1 hour (15-20 minutes if you're using a pressure cooker).
Uncover the roast and turn the flame off. Transfer the roast to a plate and discard the bay leaves. Transfer the onions, chiles, tomato and cinnamon stick to a blender. Add the cumin, cloves, oregano, sugar, vinegar, lime juice and some of the cooking liquid to a blender and pulse for about 1 minute.
Preheat the oven to 325°F. Place the roast back in the pot and strain the puree over the meat. Discard any bits left behind in the strainer. Top the beef off with just enough broth to cover it. Taste the liquid and add more salt if needed. Braising instructions: cover the pot and braise the beef in the oven for 1.5 hours. Reduce the the oven temperature to 275°F and continue braising for another 1.5-2 hours. Pressure cooker instructions: pressure cook for 45 minutes total.
Transfer the roast to a cutting board and shred it. The beef should be tender enough where all you need is a fork to break it apart. Place the shredded meat in a covered container and leave the consommé in the pot so you can dip the tortillas in later.
Prepare the pickled onions by slicing the red onions and placing them in a small bowl. Pour 1 cup of boiling water and ¼ cup of vinegar over them. Add 1 tablespoon of sugar, stir and let sit for 10 minutes then drain. Chop the cilantro and cut the limes into wedges and set aside. Shred the monterey jack cheese.
Heat a greased non-stick skillet over medium heat. Dip one tortilla at a time into the consommé, fry each tortilla until it crisps up slightly, flip and fry the other side. Add your desired amount of beef and monterey jack cheese to the center of each tortilla. Fold the tortilla over to create a taco, and fry until crispy on both sides. Transfer the tacos to a baking sheet and keep them in a warm oven while you fry the rest.
Serve the birria tacos on a platter and top them with pickled onions, fresh cilantro and crumbled cotija cheese. Garnish with lime wedges and serve with consommé for dipping.