Line a half sheet pan with a nonstick rubber mat. Spray the borders with nonstick cooking spray. Place a 25cm / 10in by 38cm / 15in by 3-mm / .13-in Plexiglas frame on the nonstick rubber mat.
Sift together the confectioners’ sugar and peanut flour. Make a French meringue with the egg whites and granulated sugar by whipping the egg whites at high speed. Once the egg whites have quadrupled in volume, pour the sugar in slowly down the side of the mixing bowl. Whip the meringue to medium-stiff peaks and fold it into the dry ingredients.
Spread onto the prepared sheet pan. Even out the batter with the top of the frame. Carefully remove the frame.
Bake until crispy and golden brown on the surface, about 6 minutes.
Cool to room temperature, then place in the freezer to harden.
Once frozen, flip the cake over onto a sheet of parchment paper. Cut it into two 14.5-cm / 5.75-in circles.
Pour a small amount (about 60g / 2.12oz) of melted milk chocolate on the smooth side of each cake. Spread into a very thin and even layer.