Line a baking sheet with a silicone baking mat.

Beat egg whites in the bowl of a stand mixer fitted with a whisk attachment until foamy. Add white sugar and beat until egg whites are glossy, fluffy, and hold soft peaks.

Sift confectioners' sugar and ground almonds in a separate bowl; quickly fold almond mixture into egg whites, about 30 strokes.

Spoon a small amount of batter into a plastic bag with a small corner cut off and pipe a test disk of batter on the prepared baking sheet. If the disk of batter holds a peak instead of flattening immediately, gently fold batter a few more times and retest.

When batter is mixed enough to flatten immediately into an even disk, spoon into a pastry bag fitted with a plain round tip. Pipe batter onto the baking sheet in rounds, leaving space between the disks.

Let piped cookies stand out at room temperature until they form a hard skin on top, about 1 hour.

Preheat the oven to 285°F (140°C).

Bake cookies in preheated oven until set but not browned, about 10 minutes.