On a large tray spread the sea salt to give a thin layer the put the potatoes on the tray. Cover with foil and bake in the oven until soft. I prefer this method to boiling as it helps prevent the potatoes being too wet and difficult to work with later.
When the potatoes are cooked allow to cool slightly then scoop out of the skins and push through a sieve into a clean bowl. This is much easier to do when potato is still hot. Set aside and allow to cool.
Meanwhile put a large pot of water on to boil and heavily salt.
Weigh out 500g of the potato and discard the rest. Add the sifted flour and Parmesan and mix well. Add the egg yolks and mix to a soft but not sticky dough. Roll out into 10g balls, then roll eack ball down the prongs of a fork to shape and place on a tray lined with baking parchment.
To cook, drop a little at a time into the simmering water. Remove the gnocchi as soon as they float, this usually takes about 1 minute. Place in a bowl with the melted butter and season. Repeat for the rest of the mix.
Alternatively the gnocchi can be made ahead of time and reheated for service by dropping into simmering water of 1 minute. Instead of putting into the bowl with butter they can be dropped into iced water to cool then dried off and kept in the fridge for up to 48hrs.