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In an electric stand mixer fitted with a dough hook, make the
détrempe by mixing ½ cup (130 g) of water with the salt, vinegar,
butter, and flour for about 15 minutes, until a smooth dough forms.
Roll out the détrempe to a thickness of ⅜ inch (10 mm), making a
15-inch (38-cm) square. Place the détrempe in the middle of the
beurre manié, then fold over each edge to encase the détrempe.
Make the dough with four simple turns. Start by rolling out the dough,
then fold it over on itself to make the first turn. Refrigerate for 1 hour.
Repeat this process a second time. Then make the next two turns,
sprinkling the dough with a mixture of brown sugar and piloncillo
sugar each time. Make sure to refrigerate for 1 hour between each
turn. Using a rolling pin, roll out the dough to a thickness of ⅛ inch (4
mm).
For assembly and finishing
Preheat the oven to 360°F (180°C). Cut 5½ by 3-inch (14 by 7.5-cm)
strips of the puff pastry dough. Twist each strip once, then place
them overlaying side by side to form a circle, and pinch together in
the center. Place in a round nonstick cake pan. Bake in the oven for
20 minutes. Remove from the oven and let cool on a rack.