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Scale all the ingredients for the dough into the bowl of a stand mixer. Mix on low speed for 2 minutes. The dough should come together at this time. Increase mixing speed to medium, and mix for another 15-20 minutes, until the dough has strong gluten development. (You should feel resistance when you pull on it.)
Remove dough from the bowl, and form into a flat, 8-inch x 8-inch square before wrapping in plastic wrap. Freeze for ~ 1 hour, until very cold, and slightly hardened. Flip the dough halfway through, so that it is evenly chilled.
In the meantime, combine sugar and salt; mix well, and set aside. In a folded over piece of parchment, use a rolling pin to shape the butter into an 8-inch x 8-inch square. Use a dough scraper to straighten the sides, as necessary. Refrigerate ~ 20 minutes, until firm but still pliable.
Once the dough and butter are both sufficiently chilled, roll out the dough as necessary to even out the thickness, and ensure that it has the same dimensions as the butter block. Then, place the butter inside the dough so that it forms a diamond within the square. Fold the edges of the dough into the middle, completely enclosing the butter. Pinch seams together.
Roll this square packet until it is three times as long, keeping roughly the same width. You will end up with an 8.5-inch x 24-inch rectangle. Fold the rectangle into thirds. This is called “the first turn.” Rotate 90 degrees, and repeat the process once more.
After the second turn, wrap the dough in plastic wrap, and chill in the freezer for ~ 10 minutes. Once cold, remove from the freezer and do one last fold, incorporating the sugar this time. (See video for details.)
Rotate 90 degrees, and roll out the dough into a rectangle, 10 inches wide x 16 inches. Cut dough into 2-inch strips, and roll each one up before placing in a greased muffin tin, or greased ring mold.
Let rise for 45-60 minutes. Preheat oven to 375 F. Bake for 45-60 minutes until golden brown. Check bottoms to make sure that dough is fully cooked; they should be golden brown as well. Remove from the oven, and use tongs to carefully remove the kouign-amanns from their muffin tin, or molds. This step should be done immediately, or else the sugar will harden into a caramel, making it impossible to extract the kouign-amanns later. Bon appetit!