Warm the milk. Gently warm the dough milk to 95–100°F (35–38°C), not above 104°F (40°C). Put two-fifths of this milk into a small bowl and stir in the dry yeast and sugar. Leave for about 5 minutes; a large foam cap is not essential. Reserve the remaining milk for the dough.
Mix and knead. Combine the dough flour and salt. Add the yeast mixture, remaining dough milk, sunflower oil, and dough egg. Mix until no dry flour remains, then knead for 8–10 minutes, until smooth, elastic, and soft, with slight tackiness. Do not add the separate rolling flour while kneading. Use separate mixer batches if the selected quantity exceeds your machine’s capacity.
Let the dough rise. Round the dough, return it to the bowl, and cover. Leave at warm, draft-free room temperature for about 60 minutes, until close to doubled. Judge the expansion rather than forcing the dough to fit the clock.
Mix the filling. During the first rise, mash the thoroughly drained feta finely with a fork. Mix in the filling egg and Schmand until thick and uniform. Do not add salt. Cover and refrigerate at 40°F (4°C) or below until needed. Do not taste the raw egg filling or dough.
Prepare and divide. Line large baking sheets with parchment rated for the baking temperature. Keep the measured rolling flour separate for a light dusting only. Gently press out very large gas bubbles, then divide the dough into equal rounds of about 450 g (16 oz) each, keeping the same portion size when scaling. Each round will make eight rolls; cover the portions you are not working on.
Roll and cut. Roll each round into an even circle about 12–12½ inches (30–32 cm) across and 3/16–¼ inch (5–6 mm) thick, using the measured dusting flour sparingly. Quarter the circle, then halve each quarter to make eight similar triangles. Repeat with the remaining dough rounds.
Fill and shape. Distribute the filling evenly across the selected number of rolls, about 20–21 g (¾ oz) per triangle. Place it near the wide end, leaving a small border at the base and sides. Fold the side corners slightly inward over the filling, then roll from the wide edge toward the point without squeezing tightly. Place point-side down and bend gently into a crescent.
Proof the rolls. Arrange on the prepared sheets with at least ¾ inch (2 cm) between rolls; use extra sheets rather than squeezing them together. Cover loosely and allow about 20 minutes, until visibly plumper. Preheat the conventional oven to 375°F (190°C), with a rack in the lower-middle position. For sequential batches, refrigerate later shaped trays, then allow them to complete their final proof before baking.
Glaze and top. Whisk the separate wash egg with its measured milk. Gently brush the proofed rolls, distributing the wash across the full yield, and sprinkle with sesame seeds. Keep wash refrigerated between batches and discard leftover wash; do not reuse it as a finishing glaze.
Bake through. Bake one tray at a time for about 20–22 minutes, checking the color around 17 minutes. If the tops brown early, tent loosely with foil and continue baking. Look for golden tops, a fully baked underside, and set, fluffy dough without a wet seam beside the filling. The egg-containing filling should reach at least 160°F (71°C) in the center of a roll; check representative rolls with a food thermometer. Color alone does not prove the center is cooked. Repeat with the other trays.
Butter and rest. Melt the finishing butter gently during the last baking minutes. Brush it thinly over the hot rolls, sharing the measured amount across all batches. Loosely cover each batch with a clean kitchen towel for about 10 minutes. Serve warm, or uncover and cool on a rack, then refrigerate promptly as directed in the notes.