For the filling:

1. In a large pan, heat the olive oil and sauté the leek and onion. Add the mushrooms and cook until they release all their moisture. Stir in the chopped meat and cook briefly. Add the pepper, corn, and tomato. Sauté for 1–2 minutes, then mix in the parsley and salt. Stir well and cook until all the liquids have evaporated. Remove from heat and stir in the cheeses until evenly distributed.

For the pie:

1. Brush a 24x33cm rectangular baking dish with a little olive oil. Lay down one phyllo sheet and drizzle with olive oil. Repeat this step with 3 more sheets, layering them. Spread the filling evenly over the base. Cover with the remaining 3 phyllo sheets, brushing each one with olive oil. Pour any leftover oil on top. Trim the excess pastry and fold the edges inward.
    
2. Cut the pie into 12 pieces and sprinkle with sesame seeds. Bake in a preheated oven at 180°C (fan setting) for 45 minutes, until golden brown.