Portuguese Egg Tarts

1. Prepare the Dough:
* Whisk butter until creamy.
* Combine flour, water, and salt; knead until tacky.
* Roll dough into a ½-inch-thick rectangle, rest for 15 minutes.
* Roll into a 15-inch square, spread a third of the butter, fold, and seal.
* Repeat with remaining butter, rolling into an 18-inch square.
* Roll into a log, wrap, and refrigerate for at least 2 hours.
2. Make the Filling:
* Boil sugar, water, and cinnamon stick for 1 minute, then let sit.
* Heat 1 cup plus 1 tablespoon milk until bubbles form.
* Whisk flour with remaining milk, then slowly add hot milk.
* Discard cinnamon stick, add sugar syrup, and cook until thickened.
* Whisk in egg yolks, strain mixture.
3. Assemble and Bake: