Preheat oven to 350F and grease a pie pan with olive oil.
Boil a large pot of water. Peel and cut plantains into quarters, to then add to the boiling water to cook for about 20 minutes, until fork tender.
While plantains cook, cook the ground beef, carrots, and onions. Add the tomato paste and oregano. Cook over medium heat for 20 minutes and season with salt and pepper to taste.
Once plantains are cooked, drain water and mash with butter and sour cream.
Place seasoned, cooked ground beef on the bottom of pie pan and top with plantain mash, making sure to cover the entire top. Sprinkle with cheese and bake for 15 minutes until bubbly and golden brown.