Preheat the oven to 425ºF. Place templates on baking sheets; line with parchment paper. Measure flour and set aside.
In a large saucepan, bring butter, water, salt, and sugar to a boil over medium-high heat. Remove the pan from the heat and add the flour all at once. Stir quickly until all the flour is incorporated, about a minute. Return to the heat and cook, stirring constantly, for another minute or two.
Transfer dough to the bowl of an electric mixer, and let cool for 5 minutes.
Add the eggs one at a time, beating well after each addition; beat until the dough loses its “slimy” look, and each egg is incorporated. (You may only need 3 eggs, depending on your climate.) The dough should be thick, but should fall slowly and steadily from the beaters when you lift them out of the bowl.
Spoon dough into a pastry bag fitted with a coupler. Attach a #10 tip (½-inch) to coupler. Pipe dough to make 12 swan necks on a baking sheet, using template as a guide. Smooth out peaks and round tops with a moistened finger; remove template. (You’re aiming for something between a numeral 2 and a question mark, with a little beak if you’re skilled and/or lucky.)
Remove the tip from the bag and pipe out 12 swan bodies on a second baking sheet, using template as a guide. These will be about 3” long, and about 2” wide. One end should be a bit narrower than the other. Smooth out peaks and round tops with a moistened finger; remove template.
Egg wash: Whisk together 1 egg and 1 teaspoon water. Brush tops of dough with egg mixture. Place swan necks on baking sheet in the freezer.
Bake swan bodies at 425° for 5 minutes; reduce oven temperature to 375°, and bake 30 minutes or until puffy and golden brown. Remove from the baking sheet to a wire rack, and cool completely.
Bake swan necks at 375° for 15 minutes or until puffy and golden brown. Remove from the baking sheet to a wire rack, and cool completely.
In a medium saucepan, combine the sugar, flour, and salt. Gradually whisk in milk. Cook over medium heat, stirring constantly until mixture starts to boil. Cook for 2 minutes until thickened.
Remove from the stove. Slowly whisk ¼ cup of the hot mixture into the beaten egg yolks, and immediately add the egg yolk mixture to the hot mixture in the saucepan. Cook for 2 more minutes, stirring constantly. Remove from heat and add butter and vanilla. Transfer the mixture to a medium bowl. Cover with plastic and refrigerate until well chilled, about 1 hour or overnight.
When pudding is chilled, whip cream to form soft peaks. Gently fold the whipped cream into the pudding until evenly mixed. Cover and chill until ready to use.
Cut swan bodies in half horizontally. Cut the top halves in half to create two wings.
Dollop or pipe a small amount of pastry cream onto the widest part of the bottom halves. Fix the swan necks in the cream. After you've put the neck in place, fill the bottom halves with additional pastry cream. Place wings on each side.
Chill until ready to serve. Sprinkle with powdered sugar before serving if desired.