Prepare the pan. Line the specified metal pan with parchment, leaving lifting overhang on two sides. Preheat a conventional oven to 400°F (200°C). Set out a larger basin and ice for prompt cooling later. At enlarged settings, use one base-size pan per multiplier and work in separate base-size batches.
Bake both pastry sheets. Divide the pastry equally into a bottom and a top for each cake. Roll each portion to about 12⅝ × 8⅝ inches (32 × 22 cm) on oven-rated parchment. Prick densely with a fork, cover with another parchment sheet, and weight with a second oven-safe baking sheet or rack. Bake each sheet for about 16–18 minutes until golden and fully baked, then cool completely on a rack. Repeat for the other sheet; allow extra baking rounds when scaling.
Trim and pre-cut the top. Trim the cooled sheets to the pan's 30 × 20 cm interior. Put one whole sheet in the pan. Cut each matching top into a 3-by-4 grid before assembly; this gives one top piece per serving for a base-size cake. Keep the pieces in order. Do not mix trimmings into the custard.
Separate and heat the whites. Separate the eggs individually. Put yolks in one bowl and whites in a completely grease-free heatproof bowl. Add the egg-white sugar and salt to the whites. Set over gently simmering water without the bowl touching it. Whisk continuously, sweeping the whole mixture, until a food thermometer registers at least 160°F (71°C) throughout; do not rely on appearance or the old lower-temperature criterion. Remove from heat and beat immediately to firm, smooth, glossy peaks. Do not continue heating into scrambled whites. Keep only briefly while finishing the custard.
Infuse the milk. Reserve one-fifth of the milk cold. Split the vanilla bean and scrape its seeds into the remaining milk with the pod. Heat gently until just below boiling, then remove the pod.
Make the yolk slurry. Whisk the yolks with the custard sugar and vanilla sugar for about 2 minutes. Add the cornstarch and flour, then gradually whisk in the reserved cold milk until smooth, with no dry pockets. Do not add dry starch directly to hot milk.
Cook the custard fully. Slowly whisk the hot infused milk into the yolk mixture, then return everything to the heavy saucepan. Cook over medium heat, whisking across the base and corners, until thick and bubbling throughout. Reduce the heat and keep it gently bubbling for 2 minutes while stirring continuously. Check that the well-stirred custard has exceeded 160°F (71°C); thickening alone is not the egg-safety check. Remove from heat and immediately sieve out small lumps if needed, before adding foam.
Fold and assemble promptly. Whisk about one-third of the heated egg-white foam into the still-hot cooked custard to lighten it. Fold the rest in two additions with a broad spatula, stopping when no large white patches remain. Immediately spread over the bottom pastry without pressing out the air. Set the pre-cut top pieces lightly in their original arrangement.
Cool with temperature checks. Begin active cooling immediately in the prepared clean ice-water bath, keeping water below the leakproof pan rim and away from the cake. Refresh the ice and check the warmest central custard with a cleaned thin probe. Transfer promptly to a refrigerator at 40°F (4°C) or below, with space around the pan and only a loose protective cover. Starting the clock at assembly, reach 70°F (21°C) within 2 hours and 41°F (5°C) or below within 6 hours total; aim for 40°F (4°C) storage. Do not leave it on the counter for a fixed cooling rest. Discard if limits are missed or cooling history is uncertain. See the monitored-cooling notes.
Chill and slice. Allow at least 6 hours in the refrigerator for the filling to set, in addition to meeting the cooling checks. Dust with the measured powdered sugar just before serving. Cut through the cream along the top-piece gaps, then saw gently through the base with a sharp knife. Wipe the blade between cuts and refrigerate remaining portions promptly.