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Make the Kouign-Amann dough following the directions for a
croissant dough on this page, using 1¾ cups (420 g) of water. When
you do the two simple turns, spread ¾ cup (5¾ ounces/162.5 g) of
melted fleur de sel butter, 1¾ ounces (50 g) piloncillo sugar (2), and
⅓ cup packed (75 g) brown sugar over the top. Fold the top third of
the dough down, and then fold the bottom third over the top.
Refrigerate for 30 minutes. Repeat the same process a second time
with the remaining ingredients. Using a rolling pin, roll to a thickness
of ⅛ inch (3.5 mm). Refrigerate for 45 minutes.
For assembly and baking
Preheat the oven to 360°F (180°C). Cut out 4¾-inch (12-cm)
squares to make an envelope fold; fold each corner of the square
into the center and cut into the middle of each side of the little
square. Place in a greased cake ring and let rest at room
temperature for 1 hour 30 minutes. Bake in the oven for 25 minutes.
Remove from the oven, remove the cake rings while hot, and let cool
on a rack.