For the tresse: Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
In a large skillet over medium-high heat, combine the butter, 2 tablespoons of the sugar and the cinnamon. Heat, stirring with a wooden spoon, until the butter is melted and bubbling and the sugar has dissolved completely. Add the apples and saute until they are starting 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 the skillet from the heat and let 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 the remaining 1/4 teaspoon sugar to make an egg wash. Set aside.
Place the puff pastry on the prepared baking sheet. Spoon the cooled apples lengthwise down the center third of the pastry, leaving 1 inch borders at the top and bottom. Using a pastry brush, brush egg wash over the exposed pastry. Using a sharp knife or pizza cutter, make diagonal cuts, 1 inch apart, in the pastry to the right and left of the apples, starting from the apples and working upwards to the edge of the pastry. Fold the top and bottom borders onto the apples and then, as if you are braiding, crisscross alternating sides of the pastry strips over each other. Your finished tart should look like a rectangle with a braided pastry top. Brush all over with egg wash and sprinkle with additional sugar.
Bake until the pastry is nicely golden and fully cooked, 20 minutes. Transfer to a wire rack to cool slightly.
For the cinnamon custard: Heat the milk and cinnamon in a small saucepan 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. While whisking, add a touch of the warm milk to the eggs. (This helps warm the eggs slightly, so they don't scramble when you add them to the milk.) Slowly add the eggs to the pan of warmed milk, stirring constantly with a wooden spoon. Return the saucepan to the heat and cook, stirring constantly, until thickened enough to coat the back of the spoon. Immediately remove from the heat 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 tresse 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 pastry 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!
Use extreme caution when igniting alcohol. Remove the pan from the heat source before adding the alcohol. Pour the alcohol into the pan and carefully ignite with a match or click lighter. Return the pan to the heat and gently swirl to reduce the flames.