Preheat the oven to 300 degrees F using the convection setting. Line 3 baking sheets with silicone mats. Measure the confectioners' sugar and almond flour by spooning them into measuring cups and leveling with a knife. Transfer to a bowl; whisk to combine.
Sift the sugar-almond flour mixture, a little at a time, through a fine-mesh sieve into a large bowl, pressing with a rubber spatula to pass through as much as possible. It will take a while, and up to 2 tablespoons of coarse almond flour may be left; just toss it
Beat the egg whites, cream of tartar and salt with a mixer on medium speed until frothy. Increase the speed to medium high; gradually add the superfine sugar and beat until stiff and shiny, about 5 more minutes.
Bake the first batch until the cookies are shiny and rise 1/8 inch to form a u0022foot,u0022 about 20 minutes. Transfer to a rack to cool completely. Repeat, using a double sheet for each batch. Peel the cookies off the mats and sandwich with a thin layer of filling (see below).