Prepare the meatballs: Mix the ground meats, onions, trahana, mint, parsley, paprika, salt, pepper and eggs in a large bowl and knead well. Shape into small meatballs, about 1 1/2-in / 4 -cm in diameter. Place on a paper-lined baking tray, cover with plastic wrap, and refrigerate for an hour for the meatballs to firm up.
Heat four tablespoons of olive oil in a large frying pan, on a low heat, and sauté the leek and the celery, stirring until they wilt, for about 7-10 minutes. Sprinkle with paprika, salt and pepper and mix well. Add the meatballs, mix it all together, and add enough water to cover 2/3 of the meatballs. Cover the pan and let them boil on a low heat until the meatballs are cooked and the vegetables are very soft, for about one hour. While the food cooks, check the pan and add more water if necessary.
A few minutes before removing the pan from the fire, add the remaining two tablespoons of butter and move the pan back and forth so that the butter melts and spreads around. Let it cool slightly and serve.