In a saute pan, melt butter and oil and saute plantains until golden brown. Remove and place on absorbent paper and season with salt and pepper
Add more oil, if needed, to saute pan and when it is hot, add onions, peppers, and garlic, and saute until onions become translucent.
Add meat and saute until meat crumbles and browns.
Add tomatoes and season lightly. Cook until meat is tender or about 10 more minutes. If meat releases too much moisture, dust with flour and cook for an additional 10 minutes.
Remove from stove, add the olives and capers, and season with vinegar Mix well and adjust seasonings as needed.
Heat a 6-inch non-stick omelet pan over medium-high heat. Add 2 teaspoons oil. When hot, add 3 to 4 ounces of meat mixture to pan and heat thoroughly.
Pour about 6 ounces (2 beaten eggs) over meat mixture in the pan to make a sort of omelet. Reduce heat to low-medium to allow egg to cook evenly. When "omelet" is firm, flip it over and let cook until firm on the other side.
Remove pan from heat and slide "omelet" out of pan onto a clean cutting board. Using a 6-inch round metal cutter, cut a neat circle out of the cooked egg. Using an offset metal spatula, place any scrap pieces cut from the egg onto the center of a heated dinner plate. Carefully place the circle of egg on top. Make a criss-cross of fried plantains on top of egg. Continue making "omelets" until all the mixture and eggs are used. Serve immediately.