Place warm water in the bowl of a stand mixer. Sprinkle with yeast and let dissolve for 10 minutes until foamy.

Add sugar and bread flour to the yeast mixture. Sprinkle with salt and add the 6 tablespoons of softened butter. Using the dough hook, mix just until butter is completely incorporated and the dough forms a ball that pulls away cleanly from the sides of the bowl, about 3-4 minutes.

Transfer dough to a lightly floured work surface and shape into a rectangle. Wrap in plastic wrap and refrigerate for at least 1 hour.

Place the chilled cup of butter between two sheets of parchment paper. Using a rolling pin, flatten it into a 6x6-inch square. Return to refrigerator to keep chilled but pliable.

On a lightly floured surface, roll the chilled dough into a 12x12-inch square. Place the butter square diagonally in the center of the dough. Fold the corners of the dough over the butter to enclose it completely. Pinch edges to seal.

Roll the dough into a 20x10-inch rectangle. Fold the dough like a letter: fold the bottom third up, then the top third down over it. Turn the dough 90 degrees. This completes one 'turn'.

Wrap the dough in plastic wrap and refrigerate for 1 hour.

Repeat the rolling, folding, and chilling process two more times (for a total of three turns). After the final turn, refrigerate the dough for at least 2 hours or overnight.

Roll the chilled dough on a lightly floured surface into a 24x8-inch rectangle about ¼-inch thick. Cut into triangles with a 5-inch base. Make a small cut in the center of each base, then roll from the base to the tip, gently stretching the dough as you roll.

Place shaped croissants on a parchment-lined baking sheet, curving the ends slightly to form the classic croissant shape. Cover loosely with plastic wrap and let rise in a warm place until noticeably puffy, about 1-2 hours.

Preheat oven to 400°F (200°C). Whisk together egg and 1 tablespoon water to make an egg wash. Gently brush over the croissants.

Bake for 18-22 minutes, or until deeply golden brown. Transfer to a wire rack to cool slightly before serving.