Preheat the oven to 400˚F. Line your baking sheet with parchment paper.
In a large skillet over medium-high heat, heat the butter, sugar and cinnamon until melted and bubbling. Using a wooden spoon, stir the mixture until the sugar dissolves completely. Add the apple slices and saute until they have started to soften, about 3 minutes. Add the Armagnac and use a long match to carefully ignite the mixture. Flambe until the flame goes out. Remove skillet from the heat and allow to cool. There should be just a little bit of liquid left in the pan.
In a small bowl, whisk together the egg yolk, water, and 1/4 teaspoon sugar to make an egg wash. Set aside.
Place your puff pastry on the lined baking sheet. Spoon the cooled apples down the center third of the pastry, lengthwise, leaving an inch at the top and bottom border. Using a pastry brush, brush the egg wash all over the exposed pastry. Using a sharp knife or pizza cutter, make diagonal cuts one inch apart on the right and left of the apples, starting from the apples and working upwards to the edge of the pastry. Fold over the top and bottom inch borders onto the apples and then, as if you are braiding, criss cross alternating sides of the diagonal pieces you have made over each other. Your finished tart should look like a rectangle with a braided pastry top. Brush all over with the egg wash and sprinkle with additional sugar.
Bake in the oven for 20 minutes or until your pastry is nicely golden and fully cooked. Remove from the oven and transfer to a wire rack to cool slightly.
While the tart is baking, make the custard. Heat the milk and cinnamon in a small pot over medium heat until just steaming. Remove from the heat. (Make sure the milk does not boil during this step. You just want to warm the milk enough to infuse it with the cinnamon flavor).
In a medium bowl, whisk together the egg yolks and sugar until pale. Add a touch of the warm milk to the eggs while you are whisking them. (This helps warm the eggs slightly so that they do not scramble when you add them to the milk). Slowly add the eggs to the pot of warmed milk, stirring constantly with a wooden spoon as you do. Return the pot to the heat and cook, stirring constantly, until it thickens (a good test is whether it coats the back of the spoon). Remove from the heat immediately and strain into a clean bowl. Cover with plastic wrap pressed directly to the surface of the custard to keep it from forming a skin. Keep warm until ready to use.
Serve the apple tart drizzled with the warm custard.
After having struggled to make puff pastry in cooking school, I am delighted that you can buy good quality puff in supermarkets these days. If you really want to test your pastry making skills, puff pastry is one to attempt. Personally, I will be buying mine from now on!