Section: How to Make Croissant Dough

1. To prepare the dough, in a stand mixer bowl, mix the flour, sugar, salt, and yeast together. Incorporate the water, milk, and softened butter. Using the dough hook, blend on speed 2 for 3-4 minutes until a smooth ball forms. Cover the bowl with plastic wrap and allow it to rise in a warm area (75-90°F) until it nearly doubles in size, about 1 ½ to 2 hours. Once risen, transfer the dough onto a plastic wrap-covered cutting board and shape it into a 10 ½-inch square. Wrap it again and refrigerate for 1-2 hours.
2. Prepare the butter by slicing it into ½-inch thick slabs. Arrange these slabs on parchment paper to create a 5-inch square. Cover with another piece of parchment or wax paper and pound the butter with a rolling pin until it measures 7 ½ inches square, adjusting as necessary. Chill until fully firm.

Section: How to Laminate the Dough

1. Begin the lamination by placing the butter at an angle over the dough, ensuring the corners of the butter touch the midpoint of each side of the dough (forming a diamond shape). Fold the dough over the butter, stretching slightly as needed to meet in the center. Seal the edges to encase the butter completely.
2. For the first turn, place the dough on a floured surface. Lightly flour the top and roll it out to a rectangle measuring 8 by 24 inches, keeping the edges straight. If the shape distorts, press the corners back into place. Fold the dough into thirds, brushing off excess flour, and freeze for 20 minutes or refrigerate for 1 hour.
3. For the second turn, repeat the rolling and folding, this time rolling towards the two open ends until the dough measures 8 by 24 inches again. Fold into thirds and freeze for 20 minutes or refrigerate for 1 hour. You may refrigerate overnight if necessary.
4. For the third turn, roll the dough to 8 by 24 inches and fold it into thirds again. Place on a baking sheet, cover tightly with plastic wrap, and refrigerate overnight or for up to 2 days (or freeze at this stage).

Section: How to Form Croissants

1. When ready to shape the croissants, take the dough from the refrigerator and place it on a floured counter, lightly flouring the top. Use a rolling pin to press down and widen the dough, then roll it into a long, narrow strip measuring 8 inches wide by 44 inches long. If it sticks, sprinkle more flour. Lift the dough at the midpoint to allow it to shrink back slightly from both sides, then trim it to 40 inches long.
2. To cut the croissants, use a yardstick or tape measure to mark the top of the dough at 5-inch intervals (7 marks total). Shift the yardstick to the bottom and mark 2 ½ inches from the end, then continue marking at 5-inch intervals for a total of 8 marks. Cut from the top corner to the first bottom mark with a pizza cutter to create the first triangle. Continue cutting the remaining triangles, yielding 15 in total with some scraps.
3. Shape each triangle by cutting a ½-inch slit at the base. Gently stretch each triangle to about 10 inches long, then tightly roll it into a croissant shape. Arrange on two parchment-lined baking sheets, spacing them evenly. Use any leftover dough scraps to create mini-croissants.

Section: How to Bake Croissants

1. Prepare the egg wash by combining 1 egg, 1 yolk, and a pinch of salt in a small bowl, beating with a fork. Brush the egg wash over the croissants and cover the remaining wash. Allow the croissants to proof uncovered at room temperature (70-75°F) for about 1-2 hours, or until they noticeably expand in size without doubling.
2. To bake, brush the croissants again with the remaining egg wash, ensuring all surfaces are coated. Bake in a preheated oven at 425°F for 10 minutes, rotating the pans halfway through. Continue baking for an additional 8-10 minutes until they achieve a rich golden brown color. Transfer to a wire rack and let cool to room temperature before serving.