Make the dry rub: In a small bowl, combine paprika with chili powder, oregano, coriander, cumin, garlic powder, salt, and pepper.
Liberally season the beef portions with the dry rub.
Heat vegetable oil in a pot/Instant Pot. Sear the roasts (in 2 batches) until brown on all sides. Deglaze the pot with 2 tablespoons of water scrubbing any stuck bits to the bottom of the pot with a wooden spatula or spoon.
Add the beef back in, and add the beef broth. Give everything a quick stir so that the meat is covered in the liquid. Add lime juice to the broth.
If cooking over the stovetop or in a slow cooker, cook until tender on medium heat (1-3 hours, depending on the cut of meat), or for 8 hours on low in the slow cooker.
If using an Instant Pot, secure the lid and set the vent to SEALING. Select the PRESSURE COOK/MANUAL setting and set the cooking time for 55 minutes at high pressure. The Instant Pot will take around 10 minutes to come to pressure and start cooking. When the cooking program ends, quickly release the steam.
Carefully remove the lid and take the beef out to shred.
Shred the meat using 2 forks, then put it back in the Instant Pot in the sauce to soak it up.
Strain liquid from beef, and serve in tortillas with your favorite toppings.