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Sift the flour and set aside. Combine the butter, milk, water, sugar and sea salt in a medium saucepan; bring to a boil. Once boiling, remove from the heat and slowly stir in the sifted flour. Return the mixture to the stove and cook over medium heat, stirring constantly. Cook until a skin form on the bottom of the pan and the dough has dried slightly--about 5 minutes. Remove the hot dough from the pan and place into the bowl of a standing mixer, fitted with the paddle attachment. Beat the dough on medium heat until cool--about 7 minutes. Once the dough is cool, stream in the eggs, one at a time, scraping the bowl as needed. Once all of the eggs are added, cover the dough with plastic and refrigerate at least one hour, up to 2 days.
Cube the cold butter. Combine all of the ingredients in the bowl of a standing mixture fitted with the paddle attachment. Mix the streusel on low speed until a loose, crumbly dough forms. Use a rolling pin to roll the dough out as thin as you can between two sheets of parchment paper. Set aside in the refrigerator of the freezer.
Preheat the oven to 375F. Place the dough in a piping bag, fitted with a plain round piping tip. Line a baking tray with parchment paper. Pipe the pate a choux into a flat disc, slightly wider than a quarter, and 1/2” thick. Leave the piped cream puffs to dry for about 30 minutes. After drying the cream puffs, lightly brush with egg wash. Cut our rounds of the chilled streusel and place on top of the cream puffs. Place the sheet of piped cream puffs in the oven. Bake at 375°F until puffed and slightly golden, about 10 minutes. Rotate the tray, turn down the oven to 325°F and bake until the cream puffs are golden and hard on the bottom. Allow to cool completely before filling.
Whip the heavy cream until soft peaks form; set aside. Bloom the gelatin in cold water; set aside. Gently heat the milk in a pot. Once simmering, turn off the heat, add the spices, and cover. Leave to steep for 15 minutes. Strain the milk to remove the solid spices. Rescale the milk to assure you have 14 ounces. In small bowl, combine the egg yolks with half of the sugar; mix well. Add the remaining sugar to the milk. Bring the milk to a boil. Once boiling, remove the milk from the heat. Add the cornstarch to the yolk/sugar mixture and whisk well. Temper the eggs into the hot milk: using a ladle, add a small amount of the hot milk to the bowl of yolks and whisk well. Add about one third of the hot milk to the yolks, one ladle at a time, whisking well after each addition. Pour the yolk/milk mixture into the pot with the rest of the hot milk. Over medium heat, cook the pastry cream while whisking constantly. Cook until the mixture thickens and bubbles. Pour the hot pastry cream into the bowl of a standing mixture. Add the bloomed gelatin. With the paddle attachment, beat the pastry cream until cool. Once cool, fold the whipped heavy cream into the pastry cream.