Brush a cake plate with some oil. Place the rim of a springform pan (26 cm Ø) on top. Melt butter at low heat. Pour the cantuccini into a freezer bag, close the bag.
Finely crumble the cantuccini with a rolling pin. Mix crumbs and liquid butter. Pour into the cake ring and press into the cake base. Chill for about 45 minutes.
Soak gelatine in cold water. Remove 3 peach halves from the tin, dab dry and dice. Fill the rest of the peaches together with the juice into a bowl and puree.
Mix the puree, yoghurt, sugar and vanilla sugar. Squeeze the gelatine, dissolve at low heat. Stir in 3 tablespoons of peach cream by the spoonful, then stir into the rest of the cream. Chill for about 15 minutes until it starts to gel.
Whip the cream until stiff. Fold the cream first, then the whisk cubes into the whisk cream. Spread on the cantuccini base. Chill overnight.
Coarsely chop the almonds, roast them without fat until golden brown, cool them down. Wash the peach, halve, stone and cut into about 16 thin slices. Remove the cake from the edge of the mould and cut into pieces. Decorate with peach and almonds.