Make the dough: in the bowl of an electric mixer fitted with the dough hook attachment, mix the flour, salt, butter, and water on low speed for 3 minutes. The dough should come together, but still look pretty rough. Raise speed to medium and mix for 3 minutes more—the dough should form a ball, but won’t look totally smooth.

Divide the dough in half. Use one right away, and wrap the other in plastic wrap. On a (very!) lightly floured surface, roll the first half into a rectangle about 5 x 10 inches.

Set your pasta machine or rollers to the widest setting. Run the dough through the pasta machine, then fold it in half. Repeat this process 4 more times (a total of 5), continuing to run the folded dough through at the widest setting.

Unwrap the second piece of dough, and use the plastic wrap to tightly wrap up the first piece (the dough will dry out if exposed too long to air in these early stages and become harder to work with). Repeat steps 2-3 with the second piece of dough.

Unwrap the first piece of dough and place it on top of the second. Use a rolling pin to press the dough together, and roll it gently until it’s about 1/2-inch thick.

Run the dough through the pasta machine (still set to the widest setting), then fold it in half. Repeat a total of 10 times. After the final pass, fold the dough in half horizontally (from one long side to the other), then fold in half from one short side to the other.

Wrap the dough tightly in plastic wrap and refrigerate for at least 1 1/2 hours.

Quarter the dough—wrap all but one piece tightly in plastic wrap. On a (very!) lightly floured surface, roll out the dough into a rectangle about 4 x 7 inches. For the next step, you’ll want to make sure you have access to a good amount of counter space, or maybe a friend or two to help (see headnote)!

Set your pasta machine or rollers to the widest setting. Run the dough through the pasta machine. Flour the dough lightly as needed (I did not need to use flour at all for my dough). Continue passing the dough through the machine, making the setting smaller/narrower each time, until the dough is almost thin enough to see through—it will be about 4 feet long at this point. For me, this was the second to last setting on my pasta maker, but it may vary depending on yours!

Gently lay the dough down on the counter. Working the length of the dough, gently stretch it to make it slightly wider and thinner (don’t worry; it’s very sturdy, but if you get a small rip or two, you won’t be able to tell).

Spread about 1/4 (1 1/2 ounces / 3 tablespoons) of the butter (listed under “for rolling the dough”) of the butter in a thin, even layer across the dough. Starting from one of the short ends, roll the dough up into a tight spiral, leaving about 1 inch of dough unrolled up. Set aside, and cover loosely with plastic wrap.

Repeat steps 8-10 with another quarter of the dough. Again, spread another 1/4 of the butter (1 1/2 ounces / 3 tablespoons) in a thin, even layer across the dough.

Unwrap the first dough spiral that you rolled, and place the excess 1 inch of dough at the end of the new piece of dough, overlapping by about 1/4-inch. Continue to roll the spiral, now making the log even thicker by rolling up the whole length of the second piece of dough.

The log should be about 2 inches thick and about 8 inches long. Wrap the log tightly in plastic wrap and refrigerate until firm, at least 2 hours and up to overnight.

Repeat steps 8-14 with the remaining two pieces of dough.

Preheat the oven to 400°F, and line two baking sheets with parchment paper.

Remove the dough logs from the refrigerator an unwrap. Cut each log into 8 even pieces, about 1 inch thick. Working with one piece at a time, use your fingers (pressing to flatten between your fingers) to work your way around the edge of the dough, making it thinner. Continue the same motion, but work inward toward the center of the round. The idea is to make the whole piece of dough thinner but make it kind of cone shaped. As you work, you’ll feel the layers in the dough, and it’s almost as if you’re fanning them out to create the final cone shape!

Brush the surface of each pastry with melted butter, and bake until the pastries are very golden brown and crisp, 23-26 minutes. Rotate the trays front to back and between their racks halfway through baking, and brush with butter again.

Let the pastries cool for at least 10 minutes, then dust generously with powdered sugar, and serve.