Brown ground beef and onion in a skillet on medium heat until onions are tender and you see no pink ground beef. Add tomato paste and mix well.You can do this without any oil.
Add chopped parsley, chopped leaks, one half of salt, pepper, and one half of turmeric and sauté. Set aside to cool.
Wash and boil potatoes until cooked through. Drain and set aside until warm to touch. Peel potatoes when still warm.
Shred potatoes in a large mixing bowl, add one half of salt, pepper, one half of turmeric, and eggs. Mix well either with your clean hand or a large fork.
Heat oil in a large, clean skillet on medium high heat. Take a heaping tablespoonful of potato mixture, flatten it on the palm of your hand, put a tablespoonful of ground beef mixture in the middle of it, put another heaping tablespoonful of potato mixture on top of the hamburger mixture. Wet the tips of your fingers, flatten the top layer and pinch the edges of the top and bottom potato mixture closed. Make sure it is completely closed and no stuffing is showing. Gently slide it in to the skillet. Continue the process until you have four or five pirashkey in the skillet. Fry until golden brown ( about two and half minutes), use a flat spatula to gently turn it over until golden brown on both sides. This step may be intimidating at first, but gets easier once you get the hang of it. Imagine you are turning pancakes over. Remove and drain on paper towel. Repeat this step until you have used all your ingredients. Keep the finished ones in warm oven while you're completing the rest.
You can serve this as a main dish by adding your favorite steamed vegetables and a green salad. You can serve warm, half pita bread pieces also to slide the pirashkey in and eat as a wrap if you wish.