Heat the milk, lemon strip, and vanilla paste in a 3-quart / 2.8 L heavy saucepan over medium heat for about 4 minutes, until steaming at the edges. Don't let it boil.

Whisk the yolks, sugar, cornstarch, and salt in a bowl for 1 minute, until pale and thick. Pour in half the hot milk in a thin stream while whisking, then scrape everything back into the pan and remove the lemon strip.

Cook over medium heat, whisking constantly, until the cream thickens and bubbles slowly, then keep whisking for 1 more minute. Off the heat, whisk in the butter. Spread into a shallow dish, press cling film onto the surface, and refrigerate for at least 2 hours while the dough rests.

Whisk the flour and salt in a bowl. Toss in the cold butter cubes, then press each cube flat between your fingers into thick flakes. Add the ice water and mix with a fork until shaggy, then press together without kneading. You should still see butter streaks.

Roll the dough on a floured surface into a 15 x 40 cm / 6 x 16 inch rectangle. Fold it in thirds like a letter, turn it 90 degrees, then roll and fold once more. Wrap and chill for 30 minutes.

Do two more rolls and folds the same way, then wrap and chill for another 30 minutes. If the butter smears or the dough feels greasy, the layers are fusing and the shells will bake up dense, so chill it for 15 minutes before continuing.

Roll the dough into an 18 x 50 cm / 7 x 20 inch rectangle about 3 mm thick. Trim the ragged edges and cut six strips 3 cm / 1.2 inches wide.

Brush six moulds with the soft butter. Starting at the narrow tip, wind each strip around a mould, overlapping the edges by half and keeping the dough loose. Tuck the end underneath and set the shells seam side down on a 33 x 46 cm / 13 x 18 inch parchment-lined sheet pan, 3 cm apart.

Chill the shaped shells for 20 minutes. Meanwhile, heat the oven to 200 C / 390 F with a rack in the middle.

Brush the shells with the egg wash and sprinkle with the sugar. Bake for 20 minutes, rotating the pan after 10 minutes, until deep golden and the ridges look crisp.

Cool on the pan for 5 minutes, then gently twist the moulds out while the shells are still warm. Cool completely on a rack for 15 minutes.

Whisk the chilled pastry cream until smooth and spoon it into a piping bag with a 1 cm plain tip. Pipe into each shell from the wide opening until the cream reaches the tip. Dust with powdered sugar and serve within 30 minutes.