Preheat the oven to 350 degrees F. Mix the kalamata and green olives, the tomatoes, scallion, onion, mushrooms, garlic and artichoke hearts in a large bowl. Stir in both cheeses, the basil, oregano and thyme; set aside, 20 minutes. Meanwhile, beat the eggs, milk, and salt and pepper to taste in another bowl.
Brush a 10-inch glass or ceramic pie dish with some of the butter. Stack 6 sheets of phyllo dough (keep the rest covered with a damp towel) and cut the stack into a 12-inch round with a paring knife. Place 1 phyllo round in the prepared pie dish and brush with butter; continue to layer the remaining 5 phyllo rounds in the dish, brushing each piece with butter before adding the next.
Spread the olive mixture evenly in the phyllo-lined dish, then pour in the egg mixture. Cut the remaining 4 phyllo sheets into 10-inch rounds. Layer on top of the pie, brushing each piece with butter before adding the next.
Bake until the top is golden and a knife inserted in the middle comes out clean, about 1 hour. Let rest 10 minutes before slicing.
Winning Olive Recipe: Learn More about the winning cook, Celia Wallis