Prepare the pan and cheese. Drain the cheese in a strainer for 10 minutes before weighing. Heat a conventional oven to 375°F (190°C), with a rack in the middle. Brush a 14 × 10 × 2-inch pan (about 35 × 25 × 5 cm) with one-eighth of the measured oil. For larger batches, use additional pans of the same size.
Mix the smooth filling. Whisk the eggs until blended, about 1 minute. Whisk in the yogurt, sparkling water, remaining oil, and salt until smooth. Before adding cheese, weigh and reserve approximately one-eighth of this smooth mixture in a separate bowl for the surface. Keep the same proportion at every batch size.
Fold in the cheese. Crumble the drained cheese into small pieces about ½ inch across and fold into the larger bowl of filling. Leave some visible cheese pieces rather than blending everything smooth.
Line the pan. Reserve two whole sheets for the bottom and one for the top of each pan. Keep unused phyllo covered with plastic wrap and a barely damp towel so it stays flexible. Overlap the bottom sheets to cover the pan, letting the edges extend over the sides.
Crumple and dip. Loosely gather each remaining sheet, dip it individually into the cheese mixture, and let it drip for 2–3 seconds. Place the dipped sheets next to one another in the pan without squeezing or packing them down. Spread any remaining cheese filling over the crumpled sheets.
Close and coat. Fold the overhanging edges inward. Lay the reserved top sheet over the filling and gently tuck its edges down the sides. Brush the reserved smooth egg-yogurt mixture evenly over the top, including the corners.
Bake until set. Bake for about 45 minutes, avoiding opening the oven during the first 35 minutes. If the surface darkens too quickly, loosely tent with foil. The top should be golden and the middle set, with no liquid egg mixture. Check the center with a food thermometer: it must reach at least 160°F (71°C). If necessary, bake another 3–5 minutes and check again.
Rest and portion. Rest uncovered for 15 minutes on a heatproof surface. Cut each pan into approximately equal pieces and serve warm. The serving count is a piece count, not a claim that each piece is a full meal.
Yield and scaling: The base pan makes approximately 12 pieces. At 2x and 3x, use two or three comparable pans and make approximately 24 or 36 pieces. Keep the layer depth, oven temperature, and rest per pan the same. Additional pans or batches can extend elapsed time.Measures: US weights and spoon measures are rounded practical approximations. Metric preserves the source formula. Oil uses a reference of about 13.6 g per US tablespoon; fine table salt about 6 g per teaspoon. Weigh ingredients for the closest ratio match. The source egg target is approximately 220 g without shells per base batch; approximately 55 g per egg. US extra-large eggs are the closest practical size but individual weights vary.Cheese: Use drained, pasteurized cow’s-milk white cheese in brine, sold by Balkan, Eastern European, or Mediterranean grocers. Hebros Foods Bulgarian White Brined Cow’s Milk Cheese is one US-market example. Its recorded label has about 4 g fat and 370 mg sodium per 28 g; brands differ substantially in salt and fat. This is a cheese category match, not a claim that every brand behaves identically. Do not silently replace it with feta, cottage cheese, or cream cheese.Timing: The 25-minute preparation includes cheese draining and oven preheating performed alongside mixing and assembly. Baking is approximately 45 minutes, followed by 15 minutes resting: 1 hour 25 minutes total. Frozen phyllo must be thawed according to its package in advance; that passive thaw is additional.Storage: Refrigerate shallow portions promptly within 2 hours, or 1 hour above 90°F. Keep at 40°F (4°C) or colder and use within 2 days for best quality. Reheat at 325°F or higher until the center reaches 165°F (74°C). Do not leave the egg-and-cheese filling unrefrigerated for prolonged assembly.Nutrition estimate: Per one of 12 assumed equal pieces, using the exact Metric formula, all oil retained, approximately 220 g shell-free egg, USDA whole-milk yogurt (3.25% fat as the nearest generic match), Hebros Foods cow’s-milk white brined cheese (USDA FDC 2677728), and Athens 14 × 18-inch phyllo’s manufacturer label. Cheese salinity, draining, yogurt fat, sheet brands, rounding, and piece size change the result. Sodium is an estimate, not a laboratory measurement. Contains wheat, milk, and eggs. This adaptation has not been kitchen-tested.