Step 1

In a stand mixer fitted with a dough hook, mix the flour, salt, and water until a soft, pillowy dough forms that pulls away from the side of the bowl, about 30 seconds.

Step 2

Generously flour a work surface and pat the dough into a 6-inch (15-cm) square using a pastry scraper. Flour the dough, cover with plastic wrap, and let it rest at room temperature for 15 minutes.

Step 3

Roll the dough into an 18-inch (46-cm) square. As you work, use the scraper to lift the dough to make sure the underside isn’t sticking to your work surface.

Step 4

Brush the excess flour off the top of the dough, trim any uneven edges, and, using a small offset spatula, dot and then spread the left 2/3 portion of the dough with a little less than 1/3 of the butter being careful to leave a 1 inch (25 mm) plain border around the edge of the dough.

Step 5

Neatly fold the unbuttered right 1/3 of the dough (using the pastry scraper to loosen it if it sticks) over the rest of the dough. Brush off any excess flour, then fold over the left 1/3 of the dough. Starting from the top, pat down the dough with your hand to release any air bubbles, and then pinch the edges of the dough to seal. Brush off any excess flour.

Step 6

Turn the dough 90° to the left so the fold is facing you. Lift the dough and flour the work surface. Once again roll it out to an 18-inch (46-cm) square, then dot the left 2/3 of the dough with 1/3 of the butter and smear it over the dough. Fold the dough as directed in steps 4 and 5.

Step 7

For the last rolling, turn the dough 90° to the left and roll out the dough to an 18-by-21-inch (46-by-53-cm) rectangle, with the shorter side facing you. Spread the remaining butter over the entire surface of the dough.

Step 8

Using the spatula as an aid, lift the edge of dough closest to you and roll the dough away from you into a tight log, brushing the excess flour from the underside as you go. Trim the ends and cut the log in half. Wrap each piece in plastic wrap and chill for 2 hours or preferably overnight. (The pastry can be frozen for up to 3 months.)

Step 9

In a medium bowl, whisk the flour and 1/4 cup milk (60 ml) until smooth.

Step 10

Bring the sugar, cinnamon, and water to a boil in a small saucepan and cook until an instant-read thermometer registers 220°F (104°C). Do not stir.

Step 11

Meanwhile, in another small saucepan, scald the remaining 1 cup milk (237 ml). Whisk the hot milk into the flour mixture.

Step 12

Remove the cinnamon stick and then pour the sugar syrup in a thin stream into the hot milk-and-flour mixture, whisking briskly. Add the vanilla and stir for a minute until very warm but not hot. Whisk in the yolks, strain the mixture into a bowl, cover with plastic wrap, and set aside. The custard will be thin; that is as it should be. (You can refrigerate the custard for up to 3 days.)

Step 13

Place an oven rack in the top third position and heat the oven to 550°F (290°C). Remove a pastry log from the refrigerator and roll it back and forth on a lightly floured surface until it’s about an inch (25 mm) in diameter and 16 inches (41 cm) long. Cut it into scant 3/4-inch (18-mm) pieces. Place 1 piece pastry dough, cut side down, in each well of a nonstick 12-cup mini-muffin pan (2-by-5/8-inch [50-by-15-mm] size). If using classic tins, cut the dough into generous 1-inch (25-mm) pieces. Allow the dough pieces to soften several minutes until pliable.

Step 14

Have a small cup of water nearby. Dip your thumbs in the water, then straight down into the middle of the dough spiral. Flatten it against the bottom of the cup to a thickness of about 1/16 inch (1.5 mm), then smooth the dough up the sides and create a raised lip about 1/8 inch (3 mm) above the pan. The pastry bottoms should be thinner than the tops.

Step 15

Fill each cup 3/4 full with the cool custard. Bake the pastries until the edges of the dough are frilled and brown, about 8 to 9 minutes for the mini-muffin tins, 15 to 17 minutes for the classic tins.

Step 16

Remove from the oven and allow the pasteis to cool a few minutes in the pan, then transfer to a rack and cool until just warm. Sprinkle the pasteis generously with confectioners’ sugar, then cinnamon and serve. Repeat with the remaining pastry and custard. These are best consumed the day they’re made.