Drain the peach halves on a sieve and cut them in half. Grease a springform pan (26 cm Ø) and sprinkle with breadcrumbs. Line the bottom with peaches close together. Separate the eggs.
Cream softened butter, 150 g sugar, salt and lemon zest with the whisks of the hand mixer. Stir in the egg yolks one by one. Mix flour and baking powder. Alternate with buttermilk and stir in briefly.
Beat the egg white until stiff and fold in. Put the dough on the peaches and smooth it down. Coarsely chop the nuts, except for a few for decoration. Sprinkle dough with chopped nuts. Bake in the preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for about 1 hour.
Leave to rest in the mould for about 10 minutes, then remove from the mould and turn onto a cake rack. Warm the jam, pass it through a sieve and spread it on the peaches. Let the cake cool down.
In the meantime, coat aluminium foil with oil. Put the rest of the nuts on the aluminium foil. Caramelise 30 g of sugar in a pan and use a tablespoon to dribble over the nuts. Let them cool down. Dust the edge of the cake with icing sugar and decorate with caramelised nuts.