Cut the top and bottom ends off of the plantains. Make 3 slits in the skin of the plantains lengthwise. Remove the peels and cut them in half crosswise. Here is a short video that shows how to peel a green plantain.
In a large heavy-bottomed skillet over medium-high heat, warm the oil. Add the plantain halves and fry until lightly browned, approximately 2 to 3 minutes per side. Remove to paper towels to drain.
Using a heavy skillet or a flat-bottomed plate, flatten each plantain into a 1/4-inch thick round disk, or as close to round as you can get. You can do this between sheets of plastic if you want to be extra neat.
One at a time, return each plantain disk to the oil and fry until golden brown and crisp, approximately 2 to 3 minutes per side. Remove the cooked plantains to paper towels to drain.
In a mixing bowl, combine the shredded chicken, mayonnaise, cilantro, salt, and pepper. Toss until the chicken is coated.
Assemble the sandwiches by taking 2 plantain “buns” and spreading half the chicken salad on each. Top with avocado, lettuce, and tomato. Add the other plantains buns to the sandwich and enjoy with plenty of napkins.
Enjoy!