Slice plantains into thin slices lengthwise. This can be done with a knife or a mandolin.
Heat vegetable oil in a large frying pan over medium heat. Fry slices of plantains on each side for 1 1/2- 2 minutes until golden brown. Drain on a paper towel lined lined dish and fry remaining plantains.
In a large skillet cook ground beef for until browned and drain any accumulated grease in pan and set aside.
In the same pan, add green pepper, onion, and garlic and cook for 3 minutes then add sofrito. Add back ground beef, seasonings, and olives and give a good mix. Pour in the tomato sauce and simmer for 5 minutes.
Spray a square pan / baking dish with nonstick cooking spray. I used a 9X9 baking dish. Layer the bottom with long slices of fried plantains. Then pour beaten egg over top of the plantain layer. Top with meat mixture then add cheese. Repeat adding a second layer of plantains, beaten egg, beef filing, and cheese. Add a final layer of plantains then sprinkle on remaining cheese and bake in a preheated 350° oven for 25 minutes until heated all the way through and bubbly.
Allow to cool for about 15 minutes so the pastelon can set making it easier to slice.