Step 1: Carefully remove the skin from the pork shoulder ham and set it aside. Using the tip of a paring knife, make a series of cuts in the pork, each about 1/2 inch deep, 1/2 inch wide, and spaced 2 inches apart. Place a sliver of garlic and a sprig of fresh oregano in each slit.
Step 2: Combine the salt, dried oregano, granulated garlic, pepper, and sage in a bowl and stir with your fingers to mix. Sprinkle the rub all over the pork shoulder. (You may not need all of the rub; it keeps well in an airtight jar and is good to have on hand for an impromptu grill session.) Drizzle the olive oil over the seasoned pork and rub it into the meat.
Step 3: Put the pork skin back on the roast and tie it in place with butcher’s string or pin it in place with bamboo skewers.
Step 4: Make the annatto oil, if using, by heating the vegetable oil in a small saucepan over medium heat. Add the annatto seeds and cook until fragrant and brown and the oil turns bright orange, 2 to 4 minutes. Immediately strain the oil into a heatproof bowl. Discard the annatto seeds.
Step 5: To grill, Ideally you’ll grill the pork shoulder over the charcoal. If you want a smoke flavor, charcoal will give you the most pronounced result.
If you are using a rotisserie, set up the grill for spit roasting, following the manufacturer’s instructions, and preheat the grill to medium-high. Thread the pork shoulder onto the rotisserie spit, using the forked prongs to hold it in place. When ready to cook, if you are spit roasting on a charcoal grill and want a smoke flavor, toss 1 1/2 cups of wood chips or chunks on the coals. If you are using a gas grill, add the wood chips or chunks to the smoker box or place them in a smoker pouch under the grate. Attach the spit to the grill and turn on the motor.
If you are grilling using the indirect method, set up the grill for indirect grilling, place a drip pan in the center, and preheat the grill to medium. When ready to cook, if a smoke flavor is desired and you are using a gas grill, add the wood chips or chunks to the smoker box or place them in a smoker pouch under the grate. If you are using a charcoal grill, toss 2 cups of the wood chips or chunks on the coals. Place the pork shoulder, skin side up, in the center of the grate over the drip pan and away from the heat and cover the grill.
Step 6: Grill the pork shoulder until dark golden brown on the outside and completely cooking through. If you spit roast the pork shoulder with the rotisserie covered, it will take 2 to 2 1/2 hours; grilling with the rotisserie uncovered will take a little longer. if you are grilling using the indirect method it will take about 4 hours. Use an instant-read thermometer to test for doneness, inserting it into the thickest part of the meat but not touching any bones or the spit. When the pork is done the internal temperature will be 190 degrees to 195 degrees F. Start basting the pork with the annatto oil, if using, or with plain vegetable oil after the pork has grilled for 30 minutes, if spit roasting, or after 1 hour of indirect grilling. Continue basting every 30 minutes. If you are using a charcoal grill, add 1 1/2 cups of wood chips or chunks after the first and second hours. Add fresh coals to each side of the grill every hour.
Step 7: Transfer the pork shoulder to a cutting board. Remove the skin and cut it into 1-inch squares. it will crisp into cracklings as it cooks. Thinly slice the pork and serve it with the cracklings and the Sparkling Barbecue Sauce, if desired.
To maximize the ratio of crisp skin to meat, buy the shank end of the pork shoulder, sometimes called a shoulder ham or picnic ham.