225 g cold unsalted butter (2 sticks), for the butter sheet
200 g sugar (1 cup), plus more for the tin
1/2 tsp flaky salt
Soft butter for a 12-cup muffin tin
How to make it
Dough (15 min plus 1 hr): Mix flour, yeast, salt, water and melted butter into a smooth, soft dough, kneading 5 minutes. Pat into a square, wrap and chill 1 hour.
Butter sheet (10 min): Beat the cold butter between parchment into a 15 cm (6 in) square. Chill until firm but bendable.
Lock in and fold (20 min plus 1 hr): Roll the dough to a 23 cm (9 in) square, set the butter on it as a diamond and fold the corners in to seal. Roll to 20 x 50 cm (8 x 20 in), fold in thirds, chill 30 minutes. Roll and fold once more, chill 30 minutes.
The sugar fold (10 min): Mix the sugar and flaky salt. Scatter a third on the counter, set the dough on it and scatter a third on top. Roll to 20 x 50 cm and fold in thirds, with the sugar trapped inside. Work fast: sugar draws water out of the dough.
Shape (10 min): Roll on the last of the sugar to a 30 x 40 cm (12 x 16 in) rectangle. Cut into twelve 10 cm squares. Fold the four corners of each square to the middle and press, then fold the new corners in again. Butter the muffin cups well and sprinkle with sugar, and drop a pastry into each.
Proof (40 min): Cover and proof until puffy, 30 to 40 minutes.
Bake (25 min): Bake at 190C (375F) for 25 to 30 minutes, until the sugar has turned deep amber. Wait 2 minutes, then tip them out onto a rack straight away, or the caramel glues them in. Eat the same day.
Tips
Don't let the sugared dough sit around; roll and bake within the hour or it turns syrupy.
Under-caramelized kouign-amann is just a soft bun. Take it dark.