1. To prepare harissa, place caraway and cumin seeds in a small skillet over medium-high heat; cook 1 minute, stirring frequently. Place seed mixture, ancho chile pepper, and next 4 ingredients (through garlic) in a blender; process until smooth.
2. To prepare brik, place potatoes in a saucepan; cover with water, and bring to a boil. Reduce heat; simmer 10 minutes or until just tender. Drain.
3. Preheat oven to 450°.
4. Heat oil in a large nonstick skillet over medium-high heat; swirl to coat. Add potatoes, turmeric, salt, and ground red pepper (if desired); sauté 6 minutes or until edges are crisp. Add parsley and green onions; cook 2 minutes, stirring frequently. Remove from heat; cool 5 minutes.
5. Place 1 sheet of phyllo dough on a large cutting board or work surface (cover remaining phyllo to prevent drying); coat phyllo with cooking spray. Fold sheet in half like a book. Coat bottom third of phyllo with cooking spray (narrow end should be facing you). Fold bottom third up. Arrange 1/4 of the potatoes in a circle in center of the bottom (folded) third of the phyllo, creating a nest for the egg. Crack 1 egg into center of potatoes. Sprinkle 1/4 of feta over egg. Sprinkle with black pepper. Fold top third of phyllo over egg, potatoes, and cheese, folding in sides to form a packet. Place packet on a baking sheet coated with cooking spray. Repeat with remaining phyllo, potatoes, eggs, cheese, and black pepper. Combine egg white and 1 teaspoon water in a small bowl, stirring with a whisk. Brush phyllo packets with egg white mixture. Bake at 450° for 9 minutes or until golden brown and crisp. Spoon harissa evenly over brik, and sprinkle with cilantro.
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