Preheat oven to 350°F Position 2 racks in the upper and lower thirds of the oven. Line two large rimmed baking sheets with parchment paper.
Spread the walnut halves on a large rimmed baking sheet and toast in the oven for about 9 minutes, until they are golden and fragrant. Let cool slightly, then transfer the walnut halves to a work surface and finely chop them.
In a large bowl, whisk the sugar with the cocoa powder and salt. Whisk in the chopped walnuts. Add the egg whites and vanilla extract and beat just until the batter is moistened (be careful not to overbeat, or it will stiffen.).
Spoon the batter onto baking sheets in 12 evenly spaced mounds.
Bake the cookies about 20 minutes, until the tops are glossy and lightly cracked and feel firm to the touch. Shift the pans from front to back and top to bottom halfway through.
Slide the parchment paper with the cookies onto 2 wire racks to cool completely before serving.
Cookies may be stored in an airtight container for up to 3 days.