Preheat the oven to 425 degrees F. On a large piece of parchment paper, trace a circle 10 inches in diameter. Use this parchment paper to line a baking sheet, pencil side down (you should still be able to see the circle). In a large saucepan, bring the water, butter, salt, and granulated sugar to a rolling boil over medium-high heat. When it boils, immediately take the pan off the heat. Stirring with a wooden spoon, add all the flour at once and stir hard until all the flour is incorporated, 30 to 60 seconds. Return the pan to the heat and cook, stirring, 30 seconds to evaporate some of the moisture.
Scrape the mixture into a mixer fitted with a paddle attachment (or use a hand mixer). Mix at medium speed. With the mixer running and, working 1 egg at a time, add 3 of the eggs, stopping after each addition to scrape down the sides of the bowl. Mix until the dough is smooth and glossy and the eggs are completely incorporated. The dough should be thick, but should fall slowly and steadily from the beaters when you lift them out of the bowl. If the dough is still clinging to the beaters, add 1 more egg and mix until incorporated.
Using a pastry bag fitted with a large plain tip and using the pencil line as a guide, pipe the dough onto baking sheet in a ring. Pipe a second ring around the first one, hugging it so the 2 rings touch closely all the way around. Pipe a third circle, using up all the remaining dough, on the crack between the first 2 rings so that all 3 rings touch closely, forming 1 big ring with 3 parts.
Whisk the remaining egg with the water. Brush the surface of the dough with the egg wash (do not use all of it). Sprinkle the almonds over the surface. Bake 15 minutes, then reduce the heat to 375 degrees and bake until puffed up and light golden brown, about 25 minutes more. Try not to open the oven door too often during the baking. Let cool on the baking sheet. The recipe can be made up to this point up to 24 hours in advance. Hold at room temperature, lightly covered with aluminum foil.
Custard : In a medium saucepan , heat the milk and vanilla bean to a boil over medium heat. Immediately turn off the heat and set aside to infuse for 10 to 15 minutes. In a bowl, whisk the egg yolks and granulated sugar until light and fluffy. Add the cornstarch and whisk vigorously until no lumps remain. Whisk in 1/4 cup of the hot milk mixture until incorporated. Whisk in the remaining hot milk mixture, reserving the empty saucepan.
Pour the mixture through a strainer back into the saucepan. Cook over medium-high heat, whisking constantly, until thickened and slowly boiling. Remove from the heat and stir in the butter. Let cool slightly. Cover with plastic wrap , lightly pressing the plastic against the surface to prevent a skin from forming. Chill at least 2 hours or until ready to serve. The custard can be made up to 24 hours in advance. Refrigerate until 1 hour before using.
Whipped Cream: When ready to serve, whip the cream and brown sugar until stiff.
Using a long serrated knife, cut the pastry ring in half horizontally. Set the top half aside. Using a clean pastry bag , pipe the custard filling onto the bottom half. Pipe the whipped cream on top of the custard. Place the top half of the pastry lightly on the whipped cream, dust with confectioners' sugar, and serve, cut into sections.
