Direction :

1. Pour the water and milk into a measuring cup and add the egg, beating with a fork to mix. Set aside.
2. Place a large bowl near your food processor. Then put the flour, yeast, salt and sugar in the processor, and give it one quick whizz just to mix. Add the cold slices of butter and process briefly so that the butter is cut up a little. You still want visible chunks of butter about least 1/2 inch in size — about 5 short pulses.
3. Empty the contents of the food processor into the large bowl, then add in the milk-egg mixture. Use your hands or a rubber spatula to mix the ingredients together, but don’t overdo it: expect to have a gooey mess with some butter lumps pebbling it. Cover the bowl with plastic wrap, put in the refrigerator, and leave overnight or up to 4 days.
4. In the late afternoon or evening the day before you are baking the kouign-amann, take the dough out of the refrigerator, let it get to room temperature (about 15 minutes or so), and roll the dough out into a 20-inch square. (Note: Don’t worry too much about inches here — just try to roll the dough out into a large square that is relatively thin. Also, you will probably need to lightly dust your work surface with flour and add more flour as needed to your rolling pin and board. See video below for guidance.) Fold the dough square into thirds, like a business letter, turning it afterward so that the closed fold is on your left, like the spine of a book. Roll the dough out again into a large square, repeating the steps above 3 times.
5. After the three rolls, roll the dough into a 16×12″ rectangle. Sprinkle the surface with 1/4 cup sugar. Gently pat the sugar into the dough. Flip the rectangle. Sprinkle with another 1/4 cup sugar. Gently pat again. Cut the dough into 12 squares — you need a 4×3 grid. Brush excess flour from dough and surface.
6. Butter a 12-cup muffin tin. Lift corners of each square and press into the center. Fit each pinched parcel into each muffin cup. Cover with plastic wrap and place in the fridge.
7. About an hour before baking, remove pan from fridge. Preheat the oven to 375ºF. Sprinkle remainging two tablespoons of sugar over top of pastries. Bake for 20 to 25 minutes or until golden on top. Let cool briefly before serving.