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1
Combine the mashed potato and crumbled feta. Season firmly with salt and white pepper. Spread the filling on a tray and allow it to cool to cool room temperature — not refrigerator-cold, not warm. The filling is ready when it holds a shape without steam rising from it.
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2
Roll the puff pastry on a lightly floured surface to a thickness of 3–4 mm. Cut into squares of approximately 12 cm. Place a heaped tablespoon of filling on one half of each square, leaving a clear border of at least 1 cm. Fold the pastry over the filling to form a triangle. Press the edges together with moistened fingertips, then crimp firmly along the seam with the tines of a fork. A well-sealed bureka holds its shape when lifted; any gap in the seal will cause the filling to burst in the oven. This is where the dish lives or dies.
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3
Transfer the formed burekas to a parchment-lined baking tray. Pierce the top of each once with a fork to allow steam to escape. Brush the entire surface generously with beaten egg wash. Apply a second coat immediately. The surface should appear uniformly glossy with no dry patches.
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4
Scatter sesame seeds over the egg-washed surfaces and press them firmly into the wash with the flat of the hand or the back of a spoon. The seeds must be physically embedded — those that sit loose will shed in the oven. The surface should be evenly, densely seeded.
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5
Bake at 200 °C until the burekas are deep amber across the entire surface and the pastry layers are visibly separated at the cut edges. Pale gold is insufficient; deep amber is the correct colour. Remove from the oven and allow to rest for five minutes before serving — the interior continues to set.