Cretan cheeses can be difficult to find in the U.S. Try a Greek market, or cheese shops with a wide selection of international cheeses.
FOR THE DOUGH:
1 tsp. active dry yeast
2 cups flour
1 tsp. salt
3 tbsp. extra-virgin olive oil
1 tbsp. sesame seeds
FOR THE FILLING:
2 tbsp. extra-virgin olive oil
4 scallions, trimmed and finely chopped
2 lbs. lean boneless lamb shoulder, cut into 3/4'' cubes
2 tsp. ground cinnamon
Salt and freshly ground black pepper
3/4 lb. fresh myzithra; or a combination of 1/2 lb. ricotta,
drained, and 1/4 lb. feta, crumbled
6 oz. graviera, or gruyère, grated
1. For the dough: Dissolve yeast in 9 tbsp. warm water in a small bowl and set aside until foamy, 5-10 minutes. Meanwhile, combine flour and salt in a large bowl. Add yeast mixture, 2 tbsp. of the oil, and 1 of the eggs, and stir with a sturdy spoon until it holds together to form a dough. Shape into a rough ball, then transfer to a lightly floured surface. Knead dough, dusting work surface with a little flour as needed, until smooth, about 10 minutes, then shape into a ball. Grease a large bowl with 1/2 tbsp. oil, place dough in bowl, cover tightly with plastic, and set aside in a warm place for 1-2 hours.
2. For the filling: Heat oil in a large skillet over medium-high heat. Add scallions and sauté for 2 minutes, then add lamb and cook until meat juices evaporate and meat begins to fry, about 15 minutes. Add cinnamon and season to taste with salt and pepper. Cook, stirring, for 1 minute more. Set aside to cool completely. Meanwhile, put myzithra, graviera, and egg in a medium bowl and mix well. Set aside.
3. Grease a 9''-round cake pan with some of the remaining oil, then line with a 16''-long sheet of parchment, draping it over sides; set aside. Divide dough into 2 uneven balls, two-thirds for the bottom and one-third for the top. Roll out both pieces on a lightly floured surface to ⅛''-thick circles. Line bottom and sides of prepared pan with larger circle, draping it over sides. Add half of the lamb, then cover with half of the cheese. Repeat process with remaining lamb and cheese. Fold overhanging dough over filling, then place smaller circle on top and tuck overhanging dough down into pan. Brush top of dough with remaining oil, cover lightly with plastic, and set aside to rise for 45 minutes.
4. Preheat oven to 375°. Beat remaining egg in a small bowl, then brush some over dough. Sprinkle top with sesame seeds. Bake until pie is deep golden, about 1 hour. Grasp parchment to lift pie out of pan, then slide pie onto a wire rack to cool for 10 minutes. Discard parchment. Slice pie into wedges and serve warm.