In a large fry pan or skillet over medium heat cook the onions, the carrots and the leeks in the olive oil for 3-4 minutes. Stir from time to time. Add the minced meat and stir frequently, separating the meat with the wooden spoon. You could also add some water for easier separation of the meat. Cook until all the minced meat is browned and there are no raw pieces (about 10 minutes). Add salt, pepper and parsley and remove the pan from the heat. Mix well and set aside for 15 minutes to cool.
Add the eggs and about 3/4 of the yellow cheese to the cooked meat and mix well.
Grease very well a 30 cm round baking pan. You can also use a rectangular one.
Preheat oven to 200 degrees C (400 degrees F).
Stack the filo sheets on the kitchen counter. Spread some filling evenly on top of the stack. Take two sheets at the same time and roll them together with the filling to form a log. Place the log around the edge of the prepared pan. Continue placing more filling on the filo sheets and rolling 2 together, until all the pan is filled with rolls and the filling is finished.
Bake for about 25-30 minutes covered with aluminium foil. Remove the foil and bake for another 10-15 minutes or until the top starts becoming golden brown. Spread evenly the rest of the grated cheese and bake for another 4-5 minutes to melt it.