1. For the marinade: Put the cilantro, olive oil, oregano, salt, vinegar, black pepper, coriander, cumin, garlic and onions in the bowl of a food processor and blend until the mixture resembles a coarse puree. Transfer 1/2 cup of the mixture to a small bowl, cover with plastic wrap and refrigerate; this is for the sweet potatoes the following day. Set aside the remaining marinade for the pork.
2. For the pork: Cut the skin away from the pork shoulder completely using a very sharp knife. Cut slits in a crisscross pattern on top of the skin, being careful not to cut all the way through, and set aside. Make small incisions on all sides of the shoulder meat using the tip of the knife. Put the shoulder in a large bowl and rub the reserved marinade all over, making sure to get it into the small incisions. Place the skin back on top of the shoulder. Cover with plastic wrap and refrigerate overnight.
3. When ready to cook, allow the pork to sit at room temperature for 30 minutes. Position an oven rack in the center of the oven and preheat to 325 degrees F.
4. Remove the plastic wrap and put the pork fat-side up in a large roasting pan. Pour any excess marinade into the roasting pan. Sprinkle the skin liberally with salt and pepper. Cover with aluminum foil and roast for 4 hours.
5. Halve the sweet potatoes lengthwise and then slice into 1-inch-thick pieces. Toss with the reserved marinade in a large bowl. Remove the roasting pan, uncover the pork and put the sweet potatoes around the pork. Continue cooking, uncovered, until a meat thermometer registers 180 degrees F and the sweet potatoes are tender, about 1 hour. Allow the pork to rest for 30 minutes before serving.
6. While the pork is resting, increase the heat to 425 degrees F. Using pot holders, carefully place a rack at the second-highest position. Remove the skin from the pork shoulder and place it on a baking sheet. Roast until the skin starts to turn golden brown and becomes very crispy, watching carefully and turning occasionally with tongs, about 25 to 30 minutes.
7. To serve, slice the pork shoulder as thinly as you like and serve alongside the sweet potatoes and pan sauce. The crispy skin can be broken up into pieces and served with the pork.
Ask your butcher to separate the skin from the pork shoulder, but be sure it is included in your package.