<b>Make the starter dough (about 15 min):</b>  In the bowl of your stand mixer, add the flour, salt, sugar, and instant yeast, and stir with the paddle attachment.  

Add the cold cubed butter and mix for 10-20 seconds...the butter should be squished and coated in flour but will still be in very large pieces.

Then, with the mixer running, slowly drizzle in the water to hydrate. Mix for about 15-20 seconds, until a shaggy dough forms.  You may need to briefly pause the mixer to scrape around the sides, to make sure the flour incorporates.  Once or twice I've had to add an extra little drizzle of water.

Wrap your dough in plastic wrap.  I use this opportunity to "pre-shape" it into a rough small rectangle with good corners, for easier rolling out.  Put it into the freezer for 10 minutes to firm everything up. 

Meanwhile mix the sugar and salt together in a shallow, wide container and set aside.

<b>Laminate your dough (about 20 or 30 min):</b>  After that 10 minutes, unwrap your chilled dough and put it on the counter, lightly flouring both sides. Roll out to about 1/4-inch (0.5cm) thickness---quite thin!---in a rectangle that's approximately 12 inches x 8 inches (30cm x 20cm).  The short end should be facing you.

Sprinkle the entire face-up side of the dough with 1-2 tablespoons of your salt/sugar mix, and press down lightly with your hands. Fold the dough into thirds, like a letter (Fold 1). 

Then turn 90 degrees, roll out thin again and sprinkle with more sugar/salt, then fold like a letter again (Fold 2). 

Repeat this twice more (for a total of 4 turns)---roll it out, sprinkle the sugar mixture, fold, then turn.  As you're rolling and folding, add a bit of flour if you need to keep it from sticking, but as minimally as possible.  If a spot of butter gets exposed in the dough, pat some flour over it.  If at any point it gets too squishy/melty, pop it in the freezer for 5 minutes.

Once you've done the 4 folds and BEFORE the final roll out, re-wrap your pastry in plastic wrap and put into the freezer for 10 minutes to re-chill.

While it's chilling, melt the butter and leave to cool slightly.  Get your muffin tin nearby, you'll need it soon. 

<b>Assemble & prove the kouign amann (about 1 hr 15 min):</b>  For the final roll out, sprinkle your table with salt/sugar and roll out your dough for the last time to a rectangle that's about 1/4-inch thick and about 13 x 9 inches in size (or 32cm x 22cm).

Trim the edges to make sure you get clean lines and cut into six squares (square-ish) that are roughly 4-inches x 2.5-inches (10cm x 6cm).  At this point you should be able to see the lamination/layers in your dough!

Take a piece of dough, brush one side with a very thin layer of melted butter, and then place the dough, butter side down, into the sugar/salt mixture.  Brush the other side with butter and then flip it over so both sides get well-coated.

To shape your kouign amann, bring the edges of the square into the center and lightly press together, then squish into the baking tin (see photos).  It's a bit like folding those paper games when you were a teenager.
Repeat the process with the rest of your dough pieces.

Place the muffin tin onto a tray and cover loosely with plastic wrap.  Let it rise somewhere semi-warm (definitely not too warm, you don't want to melt the butter) for about 1 hour.  They won’t look very puffy or grow much, but that's totally normal.

Bake (35-45 min):  Pre-heat your oven to 375 F (about 350 convection). I've even nudged it up a bit closer to 400 F and that's turned out well...you definitely want the inside cooked.

Bake for 35-45 minutes, turning after 15 mins. They should be golden, bubbling and gorgeous. If they don’t look caramelized enough, bake for a further 5 minutes.

While they are still warm, remove pastries from the tin onto a cooling rack (a small offset spatula helps), otherwise the caramel will harden.  If you forget to do this, put the pastries back in the oven for 5 minutes to melt the caramel.

The original recipe says to cool upside down...I've tried that and right side up and can't tell a difference.

Enjoy fresh! These will last for 3 days in a sealed container and you can rewarm slightly when eating as leftovers.