In the bowl of a stand mixer, add the flour, stir in the salt then add, the yeast, water and melted butter stir to wet the ingredients. Attach the dough hook and knead on low for approximately 2 minutes. Continue to knead for about 6 minutes on speed #2. The dough should be tacky but not really sticky.
Transfer the dough to a lightly floured flat surface and form into a ball. Place the ball in a lightly greased bowl, roll the dough in the bowl, cover the bowl with plastic wrap and let it sit to rise for approximately 1 hour, until doubled in bulk in a draft free warm area.
Meanwhile, make your butter block. Place the butter between 2 pieces of parchment paper and roll to form an approximate 5½ inch (14cm) square, wrap with plastic wrap and refrigerate to chill.
Once dough has risen place on a slightly floured flat surface, then roll the dough into an approximate 8 inch (20cm) square. Place the chilled butter block on an angle in the middle of the dough and then fold the corners of the dough (like an envelope) to cover the butter completely.
Roll the butter dough into an approximate 6 x18 inch (15x46 cm) rectangle. Fold the bottom third of the rectangle into the middle, then fold the top third over that (see photos). You will have a square, wrap it in plastic wrap and refrigerate for 30 minutes.
Remove the dough from the fridge and repeat the rolling and folding 2 more times, always refrigerating the dough for 30 minutes after each roll.
The last chill, roll the dough into an approximate 6x18 inch (15x46cm) rectangle, sprinkle the dough with 1 third of the caster sugar, then fold into thirds again (making a square).
As fast as you can roll the dough into an approximate 16x12 inch (41x30 cm) rectangle. Sprinkle the dough with another 1 third of the caster sugar and cut into 12 squares (they don't have to be perfect squares, don't worry it works perfectly).
Butter a 12 medium size muffin tin, take the squares by their four corners and place them in the prepared muffin tins. Gently squeeze the corners together. Sprinkle with remaining caster sugar.
Cover the muffin pan loosely with plastic wrap, and let sit until slightly puffy, approximately 30 minutes.
Pre-heat the oven to 375F (190C). Bake for approximately 20-25 minutes, until golden brown. Check after 15-20 minutes and if they are browning too quickly then cover them very loosely (like a tent) with foil, and continue baking.
Remove them from the oven and let them cool for approximately 2 minutes then remove from the muffin tin and place on a wire rack. Let cool approximately (10 minutes) before serving. Enjoy!
Notes
I halved the recipe and it turned out perfectly, if you half it also, remember the squares and rectangles will be half the size.I would advise though if you are interested in baking bread a kitchen scale is a must, since a lot of bread recipes are in grams including this one, although I do include imperial measurements. It makes for a more accurate bake.You can make them in advance, once the pastry squares are placed in the muffin tin, cover the tin lightly with plastic wrap, refrigerate overnight. When ready to bake remove the tin from the fridge and let sit at room temperature for 1 1/2 hours. Then bake.They should be stored at room temperature and will last 1-2 days. They are of course best the day they are made.To freeze them - Individually wrap each completely cooled Kouign Amann with plastic wrap and place in a freezer bag or container. Thaw and re-heat in a 350F/180C oven for approximately 5-10 minutes before eating.