Making the Dough
In the bowl of a stand mixer fitted with a dough hook, combine the flour, sugar, yeast, and salt together.
Add in butter and turn the machine on medium low to rub in the butter to the dry ingredients until it resembles coarse breadcrumbs.
Pour in the water and knead on medium high for 5 minutes, until the dough is soft and a little tacky. You can also do this step by hand.
Place in a large greased bowl, cover with cling wrap, and let rise in a warm place for 1½ hours or until doubled in size.
Punch down the dough, cover and refrigerate for a minimum of 2 hours.
Making the Butter Block
On a large piece of parchment paper draw a rectangle 12x6-inches. Set aside.
Cream the butter, sugar and salt together by hand.
On the parchment, spread the butter as evenly as possible to fit the rectangle. Bring up the sides of parchment and use a rolling pin if necessary to even out the block (see video). Refrigerate for at least 20 minutes.
Laminating the Dough
Remove the butter block from the fridge and allow it to sit at room temperature for 10 minutes to soften ever so slightly.
Remove the cold dough from the fridge. On a floured surface, roll the dough to a 20 x 8-inch rectangle.
Place the butter block in the center third of the dough rectangle and fold the dough up like a letter.
Roll the dough into a 24 x 8-inch rectangle, and fold in thirds again, like a letter. Repeat this rolling and folding 3 more times, for a total of 4 times. (Note: if at any point the butter comes through the dough and appears to be getting very soft then refrigerate until cold.
Wrap well and refrigerate for at least 1 hour, or until very firm.
Assembly the Kouign-Amann
Grease a 12 well muffin tin with butter. Toss the 2 tablespoons of granulated sugar into the wells of the tin to coat. Set aside.
Dust your work surface with roughly half of the ½ cup (4 oz/115 g) granulated sugar and toss the remaining on top of the dough.
Roll the dough to a 12 x 16-inch rectangle and cut the dough into 12 squares.
For each square, squeeze the corners of the dough together and place in a muffin cup. Cover the filled tin with plastic wrap and allow to proof for about 45 minutes. (Note: To make them ahead, place them in the refrigerator overnight)
Baking the Kouign-Amann
Preheat the oven to 375°F (190°C)
Sprinkle the pastries with the remaining 2 tablespoons of sugar and bake for roughly 30-35 minutes, or until the pastries are a deep golden brown.
Immediately remove the Kouign-Amann from the tin and let cool completely on a wire rack before serving.
Best enjoyed the day they are baked. Store leftovers in an airtight container at room temperature, for up to 3 days.