How to make "gattò": potato cake from Naples

I once experienced a funny evening in the previous house I lived in with two Calabrian girls and girl from Naples.
The girl from Naples was often to be found in the kitchen, experimenting and attempting her mother’s recipes with our very limited equipment (which included no oven).

One of those recipes was the “gattò” – a Neapolitan country-style mashed potato quiche.

It was introduced to the region by French chefs in 1768 on the occasion of the marriage of Maria Carolina (daughter of Maria Teresa Lorena-Asburgo, wife to Ferdinand the first of Borbone).

It is not, however, a French dish, but one invented in the area using traditional ingredients and butter.
The name is an evident corruption of the French gateau, and I was expecting a French dessert the evening my housemate announced she was going to make “gattò”.

While she told a friend who was visiting the dish for the evening’s dinner, he didn’t understand what it was either and promised to bring a dish as well but of a different name.
Anyway, it turned out we ended up with two “gattòs” (his was called something else) and had to stuff ourselves with potato for a week.