Preheat the oven to 400 degrees . Place the potatoes in a large pot of cold water and boil until tender, about 15 minutes; drain. Add the stick of butter and the milk and mash. Set aside.
Place the eggs in a small saucepan and add cold water to cover by 1 inch. Bring to a boil, then turn off the heat, cover and let stand for 10 minutes. Remove the eggs and place in a bowl of ice water; when cool, peel and chop.
In a large skillet over high heat, brown the beef, stirring occasionally, for about 10 minutes. Stir in the bell pepper and onion and cook for 5 minutes. Add 1/2 cup water, the olives, cilantro, tomato paste, and salt and pepper to taste.
In a 9-by-13-inch pan, layer half the mashed potatoes, the ground-beef mixture, string beans and chopped eggs. Top with the remaining mashed potatoes, brush with the melted butter and dust with paprika. Bake until golden, about 30 minutes.