Mix and knead. Mix the dough flour and dough salt in a bowl. Gradually add the lukewarm dough water and mix to form a dough. Knead firmly for 8–10 minutes until smooth, soft, and elastic, without kneading in extra flour. It may be slightly tacky but should not remain a rough, strongly sticky mass.
Pause and knead again. Cover the dough and let it rest for 5 minutes. Knead again for about 1 minute.
Coat and rest the dough. For each pan being made, divide its dough into two similar balls. Brush the balls all over with the measured dough-coating oil, dividing the oil evenly. Set apart on a plate or tray, cover so they do not dry out, and rest for 45 minutes at room temperature.
Prepare the potato filling. Toward the end of the rest, peel and weigh the potatoes, rinse, and dry well. Coarsely grate, then gently squeeze portions by hand to remove only freely released liquid; do not wring completely dry. Mix with the prepared onion, filling oil, and black pepper. Hold back the filling salt until immediately before filling.
Heat the oven and grease the pan. Preheat a conventional oven to 410°F (210°C). Use half of the pan-and-surface oil to brush the bottom and sides of the pan or pans. Spread a clean cotton cloth on a large table and lightly dust it with part of the measured work-surface flour.
Begin stretching a sheet. Remove rings, bracelets, and watches. Set a dough ball on the cloth and roll initially to roughly 14–16 inches (35–40 cm) across. Slip the backs of your hands underneath and gently stretch from the center outward. Work gradually around the sheet, keeping the rest of the dough covered.
Stretch nearly transparent. Continue stretching until the cloth is visible through the dough and the thickness is fairly even. Avoid pulling with fingertips or forcing a resistant patch. Trim only thick edges that will not stretch thin. Small tears are acceptable; do not repeatedly rework the entire sheet.
Salt and distribute the filling. Immediately before filling, mix the filling salt through the potatoes. Allocate equal filling to each dough sheet. On a stretched sheet, arrange its filling in two even strips along opposite long edges, leaving about 1 inch (3 cm) of dough clear outside the filling.
Make two loose rolls per sheet. Fold each outer dough edge over its filling. Lift the near side of the cloth to roll that side loosely toward the middle, then repeat from the opposite side. Cut along the clear center to separate the two rolls. Do not compress them tightly.
Arrange the spiral. Place a roll seam-side down around the outer edge of the pan and continue inward with the next. Cut to manageable lengths if necessary and gently close open ends. Repeat stretching and rolling with the remaining dough and filling. Fill each pan evenly without crowding or making a deeper pile. Brush the top with the remaining pan-and-surface oil.
Bake in two stages. Bake on a lower-middle rack for 15 minutes at 410°F (210°C). Reduce to 390°F (200°C) and bake for about 25 minutes more, until evenly golden. Check the filling at an inconspicuous point with a thin knife: the potatoes must be completely tender, with no firm or crunchy center. If not, bake in additional 3–5-minute intervals before using the pour.
Boil the finishing liquid. During the final baking minutes, combine the finishing water, finishing oil, and finishing salt in a small saucepan. Bring to a full boil, then remove from the heat.
Pour over the baked pie. Carefully remove the fully baked pie from the oven. Slowly distribute the hot finishing liquid over the hot pie, moistening the spaces between the rolls as well as the surface. Take care around steam and splashes. Return to the 390°F (200°C) oven for 3 minutes.
Rest and portion. Set the pan on a wire rack, loosely cover with a clean kitchen towel, and rest for 10 minutes. Divide the whole pie into the listed servings, cutting portions into smaller pieces if desired. Serve warm; refrigerate leftovers promptly as described in the notes.