Preheat the oven to 180C (350F). Line 2 large rimmed baking sheets with a silpat liner or 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 icing sugar with the cocoa powder and salt to combine. Whisk in the chopped walnuts. Add the egg whites and vanilla extract and beat just until the batter is moistened (do not over beat the mixture or it will stiffen). Spoon a tablespoon of the batter for each cookie onto the baking sheets.
Bake the cookies for 16- 20 minutes, depending on your oven, until the tops of the cookies 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. The cookies can be stored in an airtight container for up to 3 days.