Preheat the oven to 500°F, on the convection setting if available.
In a medium saucepan, combine the sugar, cinnamon stick, and 2⁄3 cup water. Bring to a boil and boil for 1 minute. Let sit until you’re ready to use it.
Roll puff pastry log on a lightly floured surface until 1 inch in diameter. Trim the ends, then cut the log into 48 slices.
Place each slice into the cavity of a mini muffin tin, with the cut side of the spiral facing up. Use your thumb to press the center of the spiral into the bottom of the pan and continue pressing to evenly flatten the dough against the bottom and sides of the cavity, extending about 1⁄16-inch above the rim of the pan. The dough should be about 1⁄16 inch thick, with the bottom a bit thicker than the sides. Repeat with the remaining dough. Refrigerate until firm, at least 10 minutes.
While the dough chills, finish the filling: In a small saucepan, heat 1 cup plus 1 tablespoon of the milk over medium-low heat until bubbles begin to form around the edges. In a large bowl, whisk the flour with the remaining 5 tablespoons milk. Continue whisking while adding the hot milk in a slow, steady stream.
Discard the cinnamon stick from the sugar syrup and whisk the syrup into the milk mixture in a steady stream. Return to the sauce pan and cook over low heat, whisking constantly, until thickened.
Add the yolks to the mixture and whisk until well combined. Strain through a fine-mesh sieve, then pour the warm filling into the pastry shells until they’re three-quarters full.
Bake until the shells are dark golden brown and crisp, the custards are set, and the tops are blackened in spots, about 20 minutes. Let cool in the pans on wire racks for 5 minutes, then transfer to wire racks. Sprinkle with cinnamon and serve warm.