In a large saucepan combine the brine ingredients and 2 cups water. Bring to a simmer, stirring to dissolve the salt and sugar. Remove from the heat and add 4 cups water. Cool to room temperature. Transfer the brine to a large container or bowl. Submerge the pork in the brine (add more water as needed to cover). Cover the bowl and refrigerate for at least 8 hours or up to 12 hours.
In the bowl of a food processor combine all of the paste ingredients, except the oil. Process to finely chop. Add the oil and pulse to blend. The consistency should be a runny paste.
One hour before grilling, remove the pork from the brine and discard the brine. Pat the pork dry with paper towels. Butterfly the loin by slicing the loin lengthwise through the center, without piercing through the other side. Open the loin like a book, making additional incisions, if needed. Spread half of the paste on the inside of the roast. Roll the loin up and truss, tying it every 1 1/2 inch. Spread the remaining paste on the outside of the pork. Skewer the trussed roast on the rotisserie spit, securing it with the spit forks.
Before turning on the grill, put the spit on the grill and turn on the motor, to test that your food freely fits and spins on the rotisserie.
Prepare the grill for indirect cooking over medium heat (350° to 450°F). Place a drip pan in the middle of the grill on top of the cooking grates to catch the drippings from the roast.
Put the spit on the grill, start the motor spinning, and make sure the drip pan is centered beneath the pork roast.
Close the lid and cook over indirect medium heat until an instant read thermometer inserted into the thickest part of the pork loin registers 145°F (or your preferred doneness), for 45 to 60 minutes, depending on the thickness of the roast, basting occasionally with the pan juices.
Remove the spit from the grill and remove the roast from the spit. Let rest indoors at room temperature for 5 to 10 minutes before carving. Discard the trussing and cut into 1/2 inch slices.