In a pot, combine the water with the piloncillo or brown sugar and bring to a boil until the sugar is completely dissolved. Turn off the flame, add the chiles and soak for 20 minutes until soft. Make a small slit in the chiles, remove the seeds and veins carefully and let the chiles drain. Set them aside.
To make the vinaigrette, combine the sugar, salt, vinegar, olive oil, and pepper in a jar and shake well. Set aside.
Heat the corn oil in a skillet and sauté the onion and garlic. Add the tomatoes and simmer for 15 minutes. Stir in the plantains and the piloncillo or brown sugar and simmer until the plantains are completely cooked. Simmer, stirring well, until a soft paste of all the ingredients has been obtained. Remove from the stove, mix with the cheese and stuff the chiles chipotles.
Roll the stuffed chiles in the flour and salt, then shake off the excess flour. Beat the egg whites until stiff, add yolks, and beat until a batter forms. Heat the 2 cups corn oil in a heavy pot, dip the chiles in the batter, then fry them quickly until they are a light golden brown.
Serve one or two chiles on a bed of mixed lettuce with the vinaigrette over the top.