Preheat the oven to 180C/350F. Grease an 9 inch pan with butter and line the bottom with parchment paper.
In a food processor combine plain flour, ground almonds, sugar, salt, baking powder and pulse briefly to combine.
Add very soft butter and pulse again until blended. Then add eggs, buttermilk, vanilla and almond extracts and blend until smooth for about 1 minute. You will have sticky batter.
Remove stones from peaches and slice. Wash the berries and let them dry.
Pour 1/2 of the batter into the prepared pan, then scatter half of the berries, top with the remaining batter and smooth the top.
Arrange the sliced peaches around the diameter of the pan, then place the remaining berries on top.
Bake in the preheated oven for 60-70 minutes or until the cake tester comes out clean. Cool in the pan for 30 minutes. Then run a knife around the side of the pan to release the cake remove from the pan. Cool completely on wire rack.
Top with fresh berries and dust with icing sugar before serving.