In a large bowl, whisk together flour, baking powder, sugar and salt. Cut cold butter into small cubes and work it into the flour with a pastry cutter or fingertips until mixture resembles coarse crumbs with pea-sized butter pieces remaining.

Stir together yogurt and olive oil in a small bowl. Add the yogurt mixture and 2 tablespoons ice water to the flour mixture and fold until a shaggy dough forms. If dough seems dry, add remaining 1 tablespoon ice water, 1 teaspoon at a time, until it holds together when pressed.

Turn dough onto a lightly floured surface and gently knead 6–8 times to bring it together. Divide into 12 equal pieces (about 80–90 g each). Flatten each piece into a disk, stack in 2 piles of 6, wrap in plastic and chill for at least 30 minutes (up to 2 hours).

Feta & Zaatar Filling

In a bowl, combine crumbled feta and cream cheese (or labneh). Mash together with a fork until smooth but still slightly textured.

Add za'atar, chopped parsley, black pepper and 1 teaspoon olive oil. Taste and adjust za'atar or pepper as desired. Set filling in the refrigerator until ready to assemble.

Potato & Caramelized Onion Filling

Cook the potatoes

Place diced potatoes in a pot of salted cold water, bring to a boil and simmer until just tender, about 8–10 minutes. Drain well and lightly mash or roughly mash to leave some texture. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper; set aside to cool slightly.

Caramelize the onions

While potatoes cook, heat butter and olive oil in a skillet over medium-low heat. Add sliced onions and 1 teaspoon sugar. Cook, stirring occasionally, until onions are deep golden and sweet, about 20–25 minutes. If they brown too quickly, reduce heat. Season with remaining 1/2 teaspoon salt, remaining pepper and ground cumin; stir to combine and remove from heat to cool.

Fold cooled caramelized onions and chopped chives/parsley into the mashed potatoes. Taste and adjust seasoning. The filling should be cohesive but not soggy—if too wet, cook briefly to evaporate moisture or add a tablespoon of breadcrumbs to bind.

Finish & Assembly

Preheat and prepare

Preheat oven to 400°F (200°C). Line two baking sheets with parchment paper or lightly grease.

Roll and fill

Working with one chilled dough disk at a time, roll each between sheets of parchment to about 1/8-inch (3 mm) thickness. Using a 4–5 inch round cutter (or a cup), cut circles. Re-roll scraps as needed.

Place about 1–2 tablespoons of filling in the center of each circle: for half of the batch use the feta–za'atar filling, for the other half use the potato–caramelized onion filling. Do not overfill—leave a 1/2-inch border.

Brush the edge of each circle with a little water or beaten egg. Fold into desired shape: triangle, half-moon or square. Press edges to seal and crimp with a fork or fingers.

Egg wash and topping

Whisk the egg with milk to make egg wash. Brush each boreka lightly with egg wash (or brush with olive oil for a less shiny finish). Sprinkle sesame or nigella seeds if using.

Bake

Place borekas on prepared baking sheets, spacing about 1 inch apart. Bake in preheated oven for 18–22 minutes, until golden brown and puffed. Rotate pans halfway if necessary for even browning.

When baked, remove from oven and brush lightly with melted butter or olive oil for extra sheen and flavor. Let cool on a wire rack for 5 minutes before serving.