In a saucepan, combine the water, milk, sugar, salt, and butter. Bring to a boil, remove from heat, and immediately add in all the flour. Quickly stir in the flour, using a rubber spatula, and return saucepan back over medium-high heat.
Continue to stir the mixture, without stopping, until the paste is smooth, about 1-2 minutes. It will pull away from the sides of the pan and leave a thin coating of cooked paste on the bottom when ready. The texture should resemble dry mashed potatoes.
Transfer the paste to a stand mixer bowl fitted with the paddle attachment. Mix on low for the choux to cool down.
While the mixer is running on medium, gradually stream in the lightly beaten eggs. Mix until well combined. The choux should be shiny at this point.
Transfer the pâte à choux to the prepared piping bag with a round tip. Pipe out ten 2 1/2-inch choux rings onto the prepared baking sheet, leaving roughly 2 inches between each ring.
Bake the choux at 400F for five minutes, then lower the temperature to 350F and bake for 35 - 40 more minutes. They are ready when golden brown, and their insides are no longer wet. Let pastries cool before filling them.
Line a baking sheet with parchment paper and set aside.
In a medium saucepan, combine sugar and water. Heat the sugar on medium heat until it boils, for about 3 minutes. Add the nuts and stir to coat them wit the syrup. Do not stop mixing the nuts. The sugar will start to crystallize, covering the nights after 5 - 7 minutes. Continue stirring.
As the sugar caramelizes, keep an eye on it; you want to cook it to a deep amber colour. When the sugar has reached a deep amber colour, 7 - 8 minutes, take the pot off the heat and spread the nuts onto the parchment-lined baking sheet. Do this quickly as the caramel will harden as it cools.
After cooling, process the nuts with salt and vanilla in a food processor. It will take about 5 minutes for the nuts to become powdery and then turn into a paste.
In a small saucepan, heat milk on medium heat with 2 tablespoons of sugar and vanilla bean until it starts to simmer. Turn off heat, cover pot, and let mixture steep while preparing eggs.
In a medium bowl, whisk together yolks, the remaining sugar, cornstarch, and salt. Slowly pour in the hot milk while whisking the egg mixture, this will prevent the eggs from cooking.
Return mixture to the pot, while turning back the heat to medium-low. Keep whisking the mixture as it thickens, 3 - 4 minutes. The pastry cream is ready when it starts to boil.
Take the pot off the heat and whisk in the softened butter. Strain the pastry cream into a clean bowl. Cover bowl with plastic wrap to prevent a skin from forming. Let pastry cream cool before using.
Beat pastry cream in a medium bowl with a whisk until it is soft and creamy. Whisk in the praline paste until well combined. Whisk in 7 tablespoons of softened unsalted butter until mixture is creamy and blended. Fill a piping bag with star or plain tip with the mousseline and set aside until you are ready to fill the pastries.
Slice choux pastries in half as you would for a sandwich. Pipe the mousseline on the bottom half and place the top half back on. Decorate the sides with the crushed hazelnuts. Dust the tops lightly with powdered sugar before serving.