Preheat oven to 180C. Place a pan over high heat and let it get very hot. Add a little olive oil to the pan along with the mushrooms. Sauté until the edges start to become brown, sprinkle over the garlic and thyme. Set the mushrooms aside in a large bowl.
Place the same pan over high heat and let it get very hot. Add a little more olive oil and add the sliced onions and leek. Saute until they become a golden yellow. Then add the diced red peppers and continue to cook until they have softened. Then add to the bowl with the mushrooms.
Add the uncooked trahanas to the mushroom and onion mixture. Add the raw scallions and cheese, season to taste and then stir through the beaten eggs to combine well.
Rub a little olive oil in the base of a baking dish. Cover with a sheet of filo, drizzle with olive oil. Cover with another sheet of filo, drizzle with olive oil and repeat with the third leaf of filo. Add the filling and then cover with a sheet of filo, drizzle with olive oil. Repeat with the final two layers. Turn the edges that are hanging over the baking pan inward and brush them with olive oil as well as the whole surface of the pita. Score into pieces, making sure not to cut all the way down to the bottom. Sprinkle with sesame seeds and place on the highest rack in the oven. Bake for 40-50 minutes or until lightly golden. When ready, remove from oven and brush with a little more olive oil. Allow the pita to cool for 10-15 minutes before serving.