For the brine, mix the sugar and salt in a large, deep nonaluminum container. Add the water and stir to dissolve. Add the rest of the ingredients and the pork loin, then pour in enough cold water to just cover the pork. Cover and refrigerate overnight or up to 2 days.
Char the peppers over an open flame or under the broiler until blackened on all sides. Transfer to a plastic container with a lid or a paper or plastic bag. Cover the container or close the bag and let the peppers steam for about 15 minutes. Peel the skins from the peppers; then cut the peppers in half, remove the stems, and scrape out the seeds. Cut into ½-inch-thick slices. Cover with a little oil; set aside. (These will keep 1 to 2 days in the refrigerator.)
Remove the pork from the brine; discard the brine. Trim the pork of excess fat and connective tissue. Cut it into eighteen ½-inch-thick slices and pound lightly between sheets of plastic wrap. Lightly sprinkle with salt and pepper. Heat 2 tablespoons oil in a large sauté pan over high heat. Add as many pork slices as will comfortably fit in the pan and cook 3 to 4 minutes on each side; remove from the pan and keep warm. Repeat with the remaining pork slices, adding 1 to 2 tablespoons oil as needed for each batch. Pour off excess fat. Pour the stock into the pan and boil, scraping up the browned bits on the bottom, until reduced to ½ cup. Stir in the peppers, onions, lemon juice, garlic, and ¼ cup chopped cilantro. Season to taste with salt and pepper.
Return the pork slices to the pan and simmer gently until warmed through. Place 3 pork slices on each serving plate and spoon the vegetables and sauce over top. Garnish with the remaining cilantro. Serve with fried potatoes.