Adjust oven racks in the upper-third and lower-third positions. Preheat the oven to 375 degrees F. Line two baking sheets with parchment paper.
Break the almond paste into small pieces and add it to the bowl of a food processer along with the sugar, cocoa powder and salt. Process until the almond paste is very finely chopped and well incorporated with the salt and sugar. Add the egg whites and vanilla, and process until a smooth dough forms, about 30 seconds. With a small scoop or spoon, dollop the batter onto the baking sheets, 1 tablespoon at a time, spaced 2 inches apart. Top each cookie with a few almond slivers and sprinkle with sanding sugar.
Bake until the cookies have risen and cracked slightly but are still soft in the center, 13 to 14 minutes; rotate the baking sheets halfway through. Allow the cookies to cool completely on the baking sheets. Store in an airtight container.