Position an oven rack in the center of the oven and preheat to 350 degrees F. Line a baking sheet with parchment.
Finely chop 1/2 cup of the walnuts and set aside. Process the remaining 3/4 cup walnuts with 1/2 cup of the sugar in a food processor until very finely ground, about 1 minute. Add the butter and vanilla and process until smooth, 30 seconds to 1 minute. Add the flour, cocoa powder and salt and process until most of the dough forms a ball and is completely combined. Scrape the dough into a bowl with a rubber spatula and fold in the chocolate chips and reserved chopped walnuts.
Roll mounded teaspoons of the dough into 1-inch balls and space evenly apart on the prepared baking sheet. Bake the cookies, rotating the baking sheet halfway through, until cracked on top and mostly firm but still slightly springy when pressed, about 18 minutes (they will firm up out of the oven). Cool the cookies on the baking sheet for 5 minutes; you want them to be slightly warm for the first tossing in sugar.
Meanwhile, put the remaining 3/4 cup sugar in a shallow bowl or pie plate. Toss the warm cookies very gently in the sugar until evenly coated. Transfer the cookies to a wire rack to cool completely, about 30 minutes, then toss again in the sugar so they are very white. The cookies will keep in a little bit of extra sugar in an airtight container for up to 1 week.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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