Preheat the oven to 360 F.
Take a baking sheet and cover it with parchment paper. Set this aside.
Split the dough in half.
Dust lightly your working surface and your rolling pin with flour. Roll out the first half of the dough as thin as possible in a rectangle shape (it does not need to be perfect, just be careful that the shape can fit in the baking sheet). Add flour when needed to prevent sticking.
Roll lightly and carefully put the dough around your rolling pin. Unroll it over the top of your baking sheet. Roll the second half of dough approximately like the first half shape and leave it on your working surface.
Drain the apple slices, but keep the juice in a bowl to use later in the recipe. On the first half of the dough, put the drained apples. Leave space at the borders, about 1 inch.
Roll the second part of the dough like the first part and carefully put it around your rolling pin. Cover the apples with the second part of the dough. Fold the edges of the first dough over the second dough and press lightly to seal it.
In a small bowl, mix the egg with a little bit of water and brush all of the croustade evenly. Sprinkle sugar over it.
Bake for about 45 to 50 mn or until the croustade is golden. Halfway through the baking, brush the rum and drained apple juice over the top. Avoid the edges, so the juice doesn't caramelize onto the parchment paper. If it does, the croustade will be difficult to take off the parchment paper.
When the croustade is done, slide a thin spatula or knife all along the croustade to be sure that nothing sticks to the parchment paper. Eat the croustade when it is lukewarm or room temperature.