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Lumps usually mean the warm milk went in too fast, so whisk it into the yolk-sugar-cornstarch mixture gradually as the recipe says. Runny custard means it did not cook long enough: keep stirring on the heat until it visibly thickens, since the cornstarch only sets once it comes up to a boil. If lumps still appear, pass the hot custard through a sieve before covering it.

Yes, and it is the most convenient way to split the work. The recipe already requires the custard to cool completely before filling, so making it a day ahead and chilling it covered directly with plastic wrap fits perfectly. Whisk it smooth again before spooning it onto the pastry squares, as it firms up in the fridge.

Cornstarch can be swapped for the same amount of another starch such as potato or tapioca starch, though the custard may set slightly differently. For the vanilla, the seeds of half a vanilla pod steeped in the warm milk, or vanilla sugar counted toward the 50 g of sugar, both work. Avoid replacing the cornstarch with flour, since it would need longer cooking to lose its raw taste.

The most common cause is too much filling or placing it too close to the edge - leave the small border the recipe calls for so the pastry can seal. Warm or barely cooled custard is also a culprit, as it thins out and runs once the oven heat hits it. Finally, always bake the rolls seam-side down so the weight of the roll holds the seam shut.

Because they contain a milk-and-egg custard, keep leftovers covered in the fridge rather than at room temperature. They are best on baking day, since the puff pastry softens once it sits against the moist filling. To bring back some flakiness, warm them briefly in the oven at a moderate heat, let them cool, and dust with fresh powdered sugar before serving.