In a small saucepan, combine butter, 3 tablespoons (45 grams) water, milk, sugar, vanilla, and salt. Cook over medium heat until butter is melted and mixture begins to boil. Add flour, stirring vigorously with a wooden spoon. Cook, stirring constantly, until dough pulls away from sides of pan and forms a ball and a film is left on bottom of pan, 1 to 2 minutes. Remove from heat.
Transfer mixture to a medium bowl. Beat with a mixer at low speed until dough is warm to the touch, about 1 minute. Add eggs, one at a time, beating until combined after each addition. (Batter should be shiny and slowly move back together when a spatula is dragged through it; after being stirred a bit, dough should also fall off mixer attachments or spoon so excess is left hanging in a V shape.) Cover and let stand at room temperature until ready to use.
For the Vanilla Danish Puff and Vanilla Bean Glaze
In the bowl of a stand mixer fitted with the paddle attachment, beat flour, cold butter, salt, orange zest, and vanilla extract at low speed just until butter is coated with flour. With mixer on low speed, add 2 tablespoons (30 grams) ice water in a slow, steady stream, beating just until a shaggy dough comes together, 1 to 2 minutes. Turn out dough onto a lightly floured surface, and shape into a 3-inch square. Wrap in plastic wrap, and refrigerate for 30 minutes.
On a lightly floured surface, roll dough into a 10x4-inch rectangle, lightly flouring surface and top of dough as needed. Fold dough into thirds like a letter. Rotate dough 90 degrees; roll into a 10x4-inch rectangle, and fold into thirds like a letter. Repeat rolling and folding procedure once more to complete third and final turn. Wrap dough in plastic wrap, and refrigerate for at least 1 hour. (See Note.)
Preheat oven to 400°F (200°C). Line a rimmed baking sheet with parchment paper.
On a lightly floured surface, roll dough into a 14x4½-inch rectangle with rounded ends (about ¼ inch thick). Gently transfer dough to prepared pan. Using a small offset spatula, spread ¼ cup (60 grams) Pâte à Choux in an even, thin even layer on top of dough. Drag a wooden pick lengthwise through choux in a zigzagging pattern. (This will help keep Pâte à Choux from inflating too much while baking.) Place remaining ¾ cup (182 grams) Pâte à Choux in a pastry bag fitted with a medium French piping tip (Ateco #865). Pipe on top of border of rolled dough, tracing edges to create an even border. Using a wet fingertip press down any points to create a smooth border, if necessary.
Bake until puffed, about 15 minutes. Reduce oven temperature to 375°F (190°C), and bake until top is dry and an even golden brown, 15 to 20 minutes more. Let cool slightly on pan, about 10 minutes. Transfer to a wire rack; let cool completely.
Make the Vanilla Bean Glaze: in a medium bowl, stir together all ingredients until smooth and well combined. Use immediately.
Just before serving, spread Vanilla Bean Glaze evenly on top of cooled pastry. Garnish with pistachios, if desired.
Notes:
Rough puff dough can be refrigerated for up to one week before assembling final Danish.
Vanilla extract and vanilla paste can be substituted 1:1, if desired.
