For the Spanish spice rubbed pork butt: Combine the paprika, salt, coriander, fennel, mustard seeds and pepper in a bowl. Rub the entire pork with the spice mixture. Cover the pork and refrigerate overnight.
For the sherry vinegar-honey glaze: Whisk the honey, vinegar, salt and pepper in a bowl.
Prepare the Caja China according to manufacturer's directions. Drizzle the pork with oil and sprinkle with salt and pepper. Place the pork in the Caja China and roast until the pork reaches an internal temperature of 175 degrees F, about 3 1/2 hours. At 175 degrees F, begin basting the pork with the Sherry Vinegar-Honey Glaze about every 15 minutes. Removing the top of the Caja China will slow the cooking process considerably.
Cook the pork until it reaches an internal temperature of 190 degrees F, about 1 hour. Remove the pork from the Caja China and tent loosely with aluminum foil. Let the pork rest for 20 minutes before slicing or pulling.
Once you start glazing the pork, don't add too much hot charcoal to the top of the Caja China, or the glaze may burn.