Activate the yeast.
In a large bowl or stand mixer bowl, combine the warm water, sugar, and yeast. Stir and let stand for 5–10 minutes, until foamy.
Make the dough.
Add the flour, salt, and 6 tablespoons softened butter. Knead by hand or with a dough hook for about 8–10 minutes, until smooth and elastic.
Stretch a small piece gently between your fingers. It should stretch thin before tearing.
Let rise.
Shape into a ball, cover, and let rise for about 2 hours, or until doubled in size.
Prepare the butter layer.
Place the remaining 1 cup butter between sheets of parchment paper. Roll into an even square or rectangle about 1/8 inch thick.
Wrap and refrigerate. Before enclosing it in the dough, let it soften just enough to bend without cracking while still feeling cool.
Enclose the butter.
Gently deflate the dough and roll into a rectangle large enough to enclose the butter.
Place the butter in the center, remove its parchment, and fold the dough around it, completely covering it. Pinch the seams closed without leaving thick overlaps.
Wrap and refrigerate for 1–2 hours.
Roll and fold.
On a lightly floured surface, gently roll the dough into a rectangle about 18 inches long.
Fold the bottom third toward the center, then fold the top third over it, like a letter. This completes one fold.
Turn the dough a quarter turn and repeat for a total of 4 folds. Between folds, wrap and refrigerate for 30–60 minutes, or until cool and relaxed. If the butter starts softening or the dough resists rolling, chill before continuing.
After the final fold, wrap and refrigerate for at least 1 hour.
Cut and shape.
Roll the chilled dough into a rectangle approximately 18 by 12 inches. If it springs back, cover and let it rest briefly in the refrigerator before continuing.
Cut into long triangles. Make a small slit, up to 1 inch, in the center of each triangle’s wide end.
Gently lengthen each triangle without squeezing the layers. Roll from the wide end toward the tip.
Let the croissants rise.
Arrange on parchment-lined baking sheets with the tips tucked underneath, leaving room between them.
Cover loosely and let rise in a comfortably warm place for 1–2 hours, or longer as needed, until noticeably puffy and gently jiggly when the tray is moved. Avoid a hot proofing spot that could melt the butter.
Brush and bake.
Preheat the oven to 400°F.
Whisk together the egg and milk. Gently brush over the croissants without pressing down.
Bake for 10 minutes, then reduce the temperature to 375°F and bake for another 10 minutes. Continue baking if needed until deeply golden and baked through.
Cool slightly and serve.
Transfer to a wire rack and let cool for at least 15–20 minutes so the centers can set. Enjoy warm, or cool completely before using for sandwiches.