Begin by whisking the softened butter in a small bowl until it reaches a creamy, sour cream-like consistency. In the bowl of a stand mixer fitted with a dough hook, combine the flour, water, and salt. Mix on low speed, scraping down the sides of the bowl as needed, until the dough forms and feels tacky to the touch.

Transfer the dough onto a generously floured surface and shape it into a 1-inch-thick rectangle. Roll it out using a floured rolling pin into a 10-inch-long rectangle, approximately ½ inch thick. Cover the dough loosely with plastic wrap and allow it to rest for 15 minutes.

Uncover the dough and roll it out into a large 15-inch square, dusting with more flour as needed to prevent sticking. Spread one-third of the creamed butter evenly over the bottom half of the dough, leaving a 1-inch border along the edge. Fold the top half over the buttered bottom, press the edges to seal, and gently pat with the rolling pin to flatten.

Roll the folded dough out again into a 15-inch square. Apply half of the remaining butter over the bottom half, again leaving a 1-inch border. Fold the top over, seal, pat, and rotate the dough so the seam faces you. Roll it once more into a final 18-inch square.

Spread the rest of the butter evenly across the entire surface of the dough, excluding a 1-inch margin along the edges. Starting from the edge nearest you, roll the dough tightly into a log. Wrap in plastic and refrigerate for at least 2 hours, preferably overnight, until very firm.

Preheat your oven to 500°F (260°C). In a medium saucepan over high heat, combine the sugar, water, and cinnamon stick. Bring the mixture to a vigorous boil for 1 minute. Remove from heat and let it steep while you prepare the rest of the filling.

Slice the chilled dough log into thirty equal pieces, each about ½ inch thick. Place each piece into an egg tart mold or muffin tin cavity, spiral side facing up. Using your thumb, press the center down and work the dough outward, molding it up the sides until it rises just slightly above the rim (about 1/16 inch for tart molds or ¾ inch for muffin tins). Chill for 10 minutes to firm the dough.

Meanwhile, warm 1 cup plus 1 tablespoon of the milk in a small saucepan over medium heat until it begins to steam and bubbles form around the edges—this takes 4 to 5 minutes. In a separate large bowl, whisk together the flour and remaining 5 tablespoons of milk until smooth. Slowly pour the hot milk into the flour mixture, whisking constantly to avoid lumps.

Discard the cinnamon stick from the sugar syrup, then gradually incorporate the syrup into the milk mixture while whisking continuously. Return the mixture to the saucepan and cook over low heat, stirring nonstop until it thickens into a smooth custard—this should take 10 to 12 minutes.

Whisk the egg yolks into the thickened custard until fully combined and silky. Strain the mixture through a fine mesh sieve to ensure a smooth texture. Fill each tart shell with approximately 1½ tablespoons of the warm custard.

Bake the tarts for 15 to 20 minutes, or until the pastry is golden and crisp, and the custard is set with a few caramelized dark spots on top. Let the tarts rest in the pans on wire racks for 5 minutes. Carefully remove them from the molds and place on wire racks to cool slightly. Dust with ground cinnamon and serve while still warm.