Milk Chocolate and Salted Caramel Gâteau Saint-Honoré

Ingredients:
2 14-ounce packages frozen puff pastry (2 sheets; such as Dufour), thawed
1 cup (scant) all-purpose flour plus more for surface
1 cup whole milk
5 tablespoons unsalted butter
1 teaspoon sugar
1/2 teaspoon kosher salt
4 large eggs
2 cups whole milk
1/3 cup plus 1/4 cup sugar
5 tablespoons cornstarch
6 large egg yolks
3 1/2 tablespoons unsalted butter
6 ounces high-quality milk chocolate (such as Lindt or Scharffen Berger), chopped
1 1/4 cups hot pastry cream (from above)
1 teaspoon unflavored gelatin
1 1/2 cups chilled heavy cream, divided
9 tablespoons sugar
1/8 teaspoon cream of tartar
1/4 cup heavy cream
1 1/4 cups chilled pastry cream (from above)
1 cup (2 sticks) unsalted butter, room temperature
1/2 teaspoon kosher salt
1/4 teaspoon vanilla extract
Chocolate Glaze
Powdered sugar

Instructions:
Preheat oven to 375°F. Line 2 baking sheets with parchment paper. Unfold 1 puff pastry sheet on a lightly floured surface. Unfold second pastry sheet and place directly on top of first, forming 2 layers. Press slightly to adhere. Using a 10" cake pan or tart pan bottom as a guide, cut pastry with a paring knife into a 10" round. Place on 1 prepared sheet.
Bake base until puffed and deep golden brown, about 30 minutes. Let cool. DO AHEAD:Can be made 1 day ahead. Store airtight at room temperature.
For cream puffs, preheat oven to 375°F. Combine milk, butter, sugar, and salt in a medium saucepan; bring to a boil. Remove from heat and add 1 cup flour. Stir to combine. Return to medium-high heat; stir dough vigorously until a dry film forms on bottom and sides of pan, about 2 minutes.
Transfer dough to a stand mixer fitted with a paddle attachment. Add eggs one at a time, incorporating fully between additions. Scrape dough into a pastry bag fitted with a 1/2" tip or a plastic bag with 1/2" cut diagonally from 1 corner. Pipe 1"-1 1/4"-diameter rounds onto second parchment-lined sheet (there should be 25-30 rounds). Smooth any pointed tips with damp fingertips to form rounded tops.
Bake for 20 minutes. Lower temperature to 325°F and bake until golden brown and dry, 15-20 minutes. Let cool completely.
Using a sharp knife, cut a small hole in bottom of each puff. DO AHEAD:> Can be made 2 months ahead. Store airtight in freezer. Thaw before continuing.
Bring milk and 1/3 cup sugar to a simmer in a medium saucepan, stirring until sugar dissolves. Stir cornstarch and 3 tablespoons water in a small bowl to dissolve. Whisk egg yolks with remaining 1/4 cup sugar in a medium bowl. Add cornstarch mixture. Gradually whisk in hot milk mixture; return to saucepan. Whisk constantly over medium heat until thick, about 2 minutes. Remove from heat. Add butter. Whisk until melted and smooth. Divide pastry cream equally between 2 medium bowls (about 1 1/4 cups each). Press plastic wrap directly onto surface of 1 bowl of pastry cream. Chill until cold and reserve for salted caramel mousseline. Immediately use hot pastry cream for diplomat cream.
Add milk chocolate to hot pastry cream; stir until melted and smooth. Press plastic wrap directly onto surface of cream and let cool to room temperature.
Place 2 tablespoons cold water in a medium bowl. Sprinkle gelatin over; let stand for 10 minutes to soften. Bring 1/2 cup cream to a boil in a small heavy saucepan. Add hot cream mixture to softened gelatin mixture and stir until dissolved. Chill just until cold, whisking frequently, about 5 minutes. Place remaining 1 cup chilled cream in a medium bowl. Using an electric mixer, beat until peaks form. Add gelatin mixture and beat until stiff peaks form.
Fold whipped cream into chocolate mixture in 3 additions, folding just to blend between additions. Cover and chill until set, about 3 hours.
Stir 2 tablespoons water, sugar, and cream of tartar in a saucepan over medium-low heat until sugar dissolves. Increase heat to medium-high; boil without stirring, occasionally swirling pan and brushing down sides with a wet pastry brush, until deep amber color forms, about 7 minutes. Remove from heat; gradually add cream (mixture will bubble vigorously). Stir until any caramel bits dissolve and mixture is smooth. Let cool.
In a stand mixer fitted with a whisk attachment, beat reserved chilled pastry cream and caramel sauce at medium speed. Gradually add butter, 1 tablespoon at a time, beating until fully incorporated between additions. Beat in salt and vanilla. Scoop into a pastry bag fitted with a small tip or a plastic bag with 1/4" cut diagonally from 1 corner and pipe into cream puffs. Cover cream puffs and chill.
Set the puff pastry disk on a serving plate. Set half of cream puffs aside. Dip bottom of remaining cream puffs into Chocolate Glaze and arrange in a circle, chocolate side down, around the edge of the pastry, leaving a 1/2" plain border. Repeat with remaining cream puffs, layering over first row of puffs as if laying bricks. Spoon chilled diplomat cream into center of gâteau, spreading out to inner edge of cream puffs. Dust lightly with powdered sugar.