Melt the butter in a large skillet over medium heat.
Add the onions and saute until translucent, 3-5 minutes.
Add the ground meats, garlic, salt, oregano and pepper to taste.
Cook, stirring to break up the pieces, until meat has completely changed color.
Drain off fat and adjust seasonings.
Cool slightly, about 5 minutes.
Add parsley, rice, and eggs and stir well. Set aside.
Preheat oven to 375 degrees F.
Brush a 9x13 pan with melted butter.
Lay one piece of phyllo dough on the bottom, and brush with melted butter.
Repeat until you have used up half of the phyllo pastry (about 10 pieces).
Spread the meat mixture evenly over the phyllo dough.
Top with the remaining phyllo dough pieces, brushing each layer with melted butter, until all the dough is used up.
Bake for 45 minutes or until golden.