kouign amann is a classic Breton specialty, a tradition of northwestern France where it originated around 1860. The name derives from the Brittany words for cake (kouign) and butter (amann).
Combine flours, salt, sugar, yeast, and butter. Transfer mixture onto the work surface, and knead for about 8 minutes; until smooth (no extra flour needed). The temperature of the dough should be at 73/80ºF/23/27ºC. Form dough into a tight ball and place in a lightly greased container, wrap up loosely or cover with a wet kitchen towel and let rise for about an hour or until it has doubled in size. Flip over work surface and deflate dough. Fold up corners and shape into a tight rectangle. Place dough onto a previously frozen baking tray line with a silicone mat. Freeze each side for 30 minutes; this will ease the lamination process. Make butter using a freezer bag, or parchment paper. Chill.
Leave butter slab out for about 10 min prior folding. The butter should remain cool but supple. The dough and butter must be the same consistency. Flour work surface and roll out dough into a rectangle twice the size of the butter slab. Place butter slab on the dough and fold over. Roll out dough into a 28''/72cm rectangle. Brush off any excess flour and fold in four (double turn/tour double). Wrap up and refrigerate an hour or overnight to rest. Flour work surface lightly and roll out dough into a 28''/72cm rectangle. Sprinkle sugar all over, and fold into thirds (single turn/tour simple). Chill for 30 minutes to rest. Roll out dough into twice its size, and split in half. Chill one half and roll out the other half into a 9x9''/23x23cm square. Divide sheet into nine 3x3''/7.5x7.5cm squares – if using English muffin rings, divide into 3.5x3.5'' squares. Fold up the four corners of a square and place each pastry inside a greased and sugared pastry ring. Or, roll up the sugared sheet of dough tightly into a log and cut into 10 swirl portions. Do likewise with the other half of the sheet. Scraps can be baked separately. Let proof pastries until it has doubled in size.
Bake Kouign-Amann at 350ºF/180ºC for about 35 minutes. Transfer onto a wire rack and let cool. Enjoy!