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Preheat oven to 350 degrees F with rack in center. Brush 9x13-inch baking dish with olive oil.
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Place spinach in clean dish towel and squeeze out as much water as possible.
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Heat 1 Tbsp. oil in large skillet over medium heat. Add onion and ½ teaspoon salt and cook, stirring, until softened, about 5 minutes. Add garlic and cook 1 minute, until fragrant.
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Add spinach, parsley, dill, nutmeg and remaining ½ teaspoon salt; stir until well combined. Remove from heat.
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In large bowl, whisk together eggs and feta.
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Add spinach mixture to feta mixture and stir to combine.
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Place one sheet of phyllo in prepared baking dish and brush with olive oil. Add 5 more sheets, brushing each with oil. Place spinach mixture on top and spread into even layer. Top pie with 6 more sheets of phyllo dough, brushing each layer with oil. Top with sesame seeds, if desired. Trim any dough hanging over sides of pan. Using sharp paring knife, gently score top of pie by making shallow lines in surface (Note: Do not cut all the way through). Bake until golden, about 40 minutes.
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Cool for 5 to 10 minutes in baking dish, then slice to serve.