Making puff pastry: Whisk the butter until creamy, then in the bowl of a stand mixer fitted with the dough hook, combine the flour, water, and salt. Mix on low speed until the dough is sticky.
Transfer to a well-floured work surface and shape into a 1-inch thick rectangle. Using a floured rolling pin, roll the dough into a ½-inch thick rectangle, 10 inches long. Cover with plastic wrap and let it rest for 15 minutes.
Roll the dough into a 15-inch square, dusting with flour as needed. Spread one-third of the butter on the bottom half, leaving a 1-inch border. Fold the top over the butter, seal the edges, and roll into another 15-inch square. Spread half of the remaining butter on the bottom half, fold, seal, and roll into an 18-inch square. Spread the rest of the butter, leaving a 1-inch border. Roll the dough into a tight log, wrap in plastic, and refrigerate until firm for at least 2 hours or overnight.
To make the filling, preheat the oven to 500°F. In a saucepan, combine sugar, water, and a cinnamon stick. Boil for 1 minute, then remove from heat and let sit until needed.
On a floured surface, trim the dough ends and cut the log into thirty (30) ½-inch slices. Place each slice in a muffin tin or tart mold, with the cut side of the spiral facing up. Press the center with your thumb to flatten it against the bottom and sides, extending the dough slightly above the rim. Repeat with all slices and refrigerate for 10 minutes.
Heat 1 cup plus 1 tablespoon of milk in a saucepan until it bubbles, about 4-5 minutes. In a large bowl, whisk together flour and the remaining 5 tablespoons of milk. Gradually whisk in the hot milk. Remove the cinnamon stick from the sugar syrup and whisk it into the milk mixture. Return to the saucepan and cook over low heat, whisking constantly, until thickened, about 10-12 minutes.
Add the yolks to the mixture and whisk until well combined, then strain through a fine-mesh sieve. Pour 1½ tablespoons of the warm filling into each pastry shell.
Bake for 15 to 20 minutes until shells are golden brown, custards are set, and tops are lightly blackened. Cool on wire racks for 5 minutes, then remove tarts, place on racks, and sprinkle with cinnamon. Serve warm.