Dissolve yeast and sugar in warm milk in a bowl. Let stand until yeast softens and begins to form a creamy foam, about 5 minutes.
Combine 1 cup all-purpose flour, whole wheat flour, 1/2 cup water, vegetable oil, salt, and yeast mixture in the bowl of a stand mixer fitted with the hook attachment; knead until pliable and not too sticky. Add a little flour if too soft, or warm water if too hard. Cover with a wet cloth and let sit at room temperature for 45 to 50 minutes.
Preheat the oven to 350 degrees F (175 degrees C). Grease a baking tray with butter.
Mix feta cheese, parsley, salt, pepper, and chili powder together in a bowl until well combined.
Knead dough for 2 minutes. Divide it into 12 equal portions, and roll each one into a ball. Use your hands or a rolling pin to flatten each ball into a 2- to 3-inch circle. Add a spoon of cheese filling in the middles and fold the edges upward like a bundle, pressing to secure. Place on the prepared baking try, folded-sides down. Brush with milk and sprinkle with poppy seeds.
Bake on the top rack of the preheated oven until golden, 30 to 32 minutes.
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