To make the cake: Preheat the oven to 275 degrees F.
Line 2 baking sheets with parchment and draw
on 2 (9-inch) circles. Cook's Note: You could also do rectangles.
In a small bowl, combine the ground almonds, cornstarch, and all but 2 tablespoons of the sugar
. In a separate bowl, beat the whites to soft peaks, and then beat in the remaining sugar to make a stiff meringue. Fold in the almond mixture in 3 batches to combine thoroughly. Using a piping bag with a large tip, pipe the meringue
onto the circles on the parchment. Bake until crisp
and dry, about 1 1/2 hours.
To make the buttercream: Heat the sugar with 1/3 cup plus 2 tablespoons water to dissolve, then boil to soft-ball stage
, which is just before the syrup changes color (235 to 240 degrees F on a candy thermometer
). Beat the egg yolks in a stand-up mixer
, then, with the beaters running, quickly add the hot syrup in a thin stream. Continue beating until the mixture is cool and forms and thick mousse
, about 5 minutes. Beat in the butter, gradually, and finally add the vanilla.
To assemble the cake: Set a round of meringue on a serving plate. Spread over a quarter of the buttercream. Lay in a layer of sliced peaches. Spread the top layer with buttercream
and set it on top of the first. Spread the remaining butter cream over the sides of the cake
. Press the toasted almonds all around the sides. Arrange another layer of peach slices on top.