In a large pot, heat 2 tablespoons oil over medium heat. Add meat and sprinkle with baking soda and salt. Brown the meat well. Using a slotted spoon, remove the meat and reserve, leaving the rendered fat behind. Sauté the peppers and onions until softened. Add tomato paste, diced tomatoes, and sofrito. Cook for 5–10 minutes until liquids have evaporated. Add reserved meat and stir well to combine. Set aside to cool slightly.

In a large sauté pan, heat 2–3 tablespoons oil at a time and lightly fry the plantain slices until golden brown and just softened. Continue in batches until all the slices have been fried. Drain on paper towel–lined tray.

Preheat broiler. In a 13- x 9-inch glass baking dish, lay half the prepared plantain slices in slightly overlapping fashion, as you would lasagna noodles. Cover with the meat mixture. Lay the remaining plantain slices to cover the meat. Top with shredded cheese. Place in broiler just until the cheese bubbles and begins to brown.