Make the dough - In the bowl of a stand mixer, mix the flour, yeast, salt, and cardamom together. Add the cold water and knead with the dough hook attachment until a sticky and elastic dough is formed, about 5 minutes on low speed. Transfer the dough to a lightly oiled bowl, cover with plastic wrap, and let rest in a warm place for 1 hour or until doubled in size.

Prepare the butter slab - Place the sticks of cold unsalted butter on a parchment-lined tray and cover with another piece of parchment paper. Using a rolling pin, pound the butter until it forms a flat and even slab, about 8x7 inches. Place it in the fridge to chill for at least 20 minutes.

Laminate the dough - Flour your work surface, and roll out the dough into a large rectangle, roughly the same size as the butter slab. Take the butter out of the fridge, and place it on the part of the dough that is closest to you. Fold the top third of the dough over the butter, then the bottom third up over it. This is called a single turn. Turn the dough 90 degrees, and repeat the process: roll out, fold in thirds. Place the dough in the fridge to chill for 30 minutes.

Prep the sugar and cinnamon filling. - In a small bowl, mix together the sugar and cinnamon. Set aside.

Laminate the dough for the second time - Repeat the rolling and folding process described before, making sure to dust your work surface and the dough with flour as needed. Place the dough in the fridge for at least 1 hour.

Shape the kouign amann - Grease well a 9-inch cake pan and set it aside. Roll out the laminated dough into a large circle, about 1/4 inch thick. Sprinkle the sugar and cinnamon mixture over the surface of the dough, leaving a 1/2-inch border along the edges. Roll up the dough as you would for a cinnamon roll, making it a tight sausage shape. Cut the dough into 8 equal parts, and place them cut side down in the prepared pan. Cover the pan with a clean towel and let rest for 30 minutes.

Bake the kouign amann - Preheat the oven to 350°F. Brush the tops of the kouign amann with water. Bake on the middle rack of the preheated oven for 30 to 35 minutes or until golden brown and caramelized. Let cool for 10 minutes before carefully inverting them onto a plate. Serve warm or at room temperature.