Making puff pastry: Whisk the butter till creamy, then within the bowl of a stand mixer fitted with the dough hook, mix the flour, water, and salt. Combine on low pace till the dough is sticky.
Switch to a well-floured work floor and form right into a 1-inch thick rectangle. Utilizing a floured rolling pin, roll the dough right into a ½-inch thick rectangle, 10 inches lengthy. Cowl with plastic wrap and let it relaxation for quarter-hour.
Roll the dough right into a 15-inch sq., dusting with flour as wanted. Unfold one-third of the butter on the underside half, leaving a 1-inch border. Fold the highest over the butter, seal the sides, and roll into one other 15-inch sq.. Unfold half of the remaining butter on the underside half, fold, seal, and roll into an 18-inch sq.. Unfold the remainder of the butter, leaving a 1-inch border. Roll the dough into a good log, wrap in plastic, and refrigerate till agency for a minimum of 2 hours or in a single day.
To make the filling, preheat the oven to 500°F. In a saucepan, mix sugar, water, and a cinnamon stick. Boil for 1 minute, then take away from warmth and let sit till wanted.
On a floured floor, trim the dough ends and minimize the log into thirty (30) ½-inch slices. Place every slice in a muffin tin or tart mildew, with the minimize facet of the spiral going through up. Press the middle together with your thumb to flatten it in opposition to the underside and sides, extending the dough barely above the rim. Repeat with all slices and refrigerate for 10 minutes.
Warmth 1 cup plus 1 tablespoon of milk in a saucepan till it bubbles, about 4-5 minutes. In a big bowl, whisk collectively flour and the remaining 5 tablespoons of milk. Steadily whisk within the sizzling milk. Take away the cinnamon stick from the sugar syrup and whisk it into the milk combination. Return to the saucepan and prepare dinner over low warmth, whisking continually, till thickened, about 10-12 minutes.
Add the yolks to the combination and whisk till properly mixed, then pressure via a fine-mesh sieve. Pour 1½ tablespoons of the nice and cozy filling into every pastry shell.
Bake for 15 to twenty minutes till shells are golden brown, custards are set, and tops are calmly blackened. Cool on wire racks for five minutes, then take away tarts, place on racks, and sprinkle with cinnamon. Serve heat.