Preheat the 430 degrees F (220 degrees C).
Peel and core the Apple (6), either slicing them into quarters or leaving them halved.
In a cast iron skillet over low heat, melt the Salted Butter (50 gram) with the Caster Sugar (50 gram) to make a syrup then pour in the Dark Rum (50 milliliter).
Once the syrup is combined, add the apple pieces, covering them in the syrup. Cook over medium heat until just soft.
Remove the skillet from the heat and use a spoon to arrange the apples tightly around the base of the skillet. I like to have the cut-side of the apples facing up, so that when the tarte tatin is turned out the curved edges peek outwards.
Roll out the Puff Pastry (400 gram) on a surface dusted with All-Purpose Flour (to taste) and use a sharp knife to slice a circle to fit the top of the skillet. Using your fingers, push the edges of the pastry around the apple so that they fit snugly.
Brush the pastry with the Egg (1) and bake for 35 – 40 minutes or until the pastry is golden. If the pastry browns too quickly, reduce the oven’s temperature to 355 degrees F (180 degrees C).
Leave the tarte tatin for 20 minutes to cool slightly before carefully turning it out on to an inverted plate. Slice it and serve topped with a scoop of Vanilla Ice Cream (to taste) and an extra shot of rum.