Preheat the oven to 190°C/gas mark 5. Liberally butter a 22cm square baking dish, about 5 cm deep. A lasagne dish is ideal.
Mix 3 tbsp Amaretto and the sugar in a large bowl. Peel and stone the peaches and cut into thick slices. As you do so, mix them into the sugary mixture. Then transfer the peaches to the buttered baking dish.
Beat together the butter and icing sugar until pale and fluffy, then beat in the almonds, eggs, cream, remaining Amaretto and a few drops of almond extract. Pour over the peaches and bake for 30-40 minutes or until the almond mixture is firm and golden. Remove from the oven and dust with extra icing sugar.