Step 1

Preheat the oven to 350°F. Spread walnuts in a single layer on a rimmed baking sheet, and toast until light golden and fragrant, about 8 minutes. Transfer to a plate, and let cool completely. Line two baking sheets with parchment paper.

Step 2

In a food processor, combine ½ cup flour with the toasted nuts, and pulse until the nuts are finely ground. In a medium bowl, whisk together the flour-nut mixture and the remaining 1 cup flour and the salt; set aside.

Step 3

In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and ½ cup sugar until light and fluffy, about 2 minutes. Beat in vanilla. With the mixer on low speed, add the flour mixture in two batches, and beat until combined.

Step 4

Roll 1 tablespoon of dough into a 3-inch log. Using your fingers, shape log into a crescent, tapering the ends slightly so that the center is the widest part. Repeat with remaining dough, placing crescents about 1 inch apart on prepared sheets. Freeze or refrigerate until crescents are very firm, about 30 minutes.

Step 5

Bake, rotating sheets halfway through, until the edges of the cookies begin to turn golden, 16 to 18 minutes. Transfer sheets to a wire rack to cool, 5 minutes. Transfer cookies to the rack to cool completely. Place the remaining 1 cup sugar in a shallow bowl and roll cookies in it to coat completely. Cookies can be kept in an airtight container at room temperature for up to 5 days.