Step 1

Preheat the oven to 350 degrees F. Place rack in the center of the oven.

Step 2

Place 1½ cups of walnut halves on a baking sheet and toast for 8 to 10 minutes, until they begin to smelly nutty and turn pale golden inside. Remove from the oven and let cool.

Step 3

Place the cooled, toasted walnuts in a food processor and process until ground into crumbs, about 20 seconds.

Step 4

In a large bowl, use an electric mixer to beat the butter and ¾ cup powdered sugar together at medium speed until creamy and smooth and light (about 2 minutes). Reduce the mixer speed to low and add the ground walnuts, vanilla and salt. Add the flour, and mix on low for 30 seconds. Scrape and beat again until thoroughly combined.

Step 5

Line a baking sheet with parchment paper or a silpat mat. Using a ¼-cup ice cream scoop or a large spoon, scoop the dough into ¼ cup-sized balls and place on the prepared baking sheet a few inches apart. Lightly press each with the palm of your hand to flatten slightly. Press an untoasted walnut half into the center of each cookie. Bake for 18 to 22 minutes, until the cookies are light golden brown. Remove from the oven and let cool completely on the baking sheet on a wire rack.

Step 6

Using a sifter or small sieve, dust the cookies with the remaining ½ cup powdered sugar until they are completely white.

Step 7

Store cookies in an airtight container at room temperature for up to 3 days. Dust with additional powdered sugar to freshen them up before serving.