Put butter cut into pieces, sugar and salt in a small saucepan with a thick bottom and heat it over low heat, stirring, until the butter is melted. Then continue to bring the mixture to a boil over low heat, stirring, and simmer until slightly thickened, about 5 minutes.
Take the butter-sugar mixture off the heat, add honey, baking soda and rum and stir. Place the mixture back on the stove and heat (don't boil!) it over low heat, stirring, for about 5 minutes, until it turns a very light caramel color.
Take the honey mixture off the heat and let it cool to warm.
Stir in eggs to the honey mixture.
Add flour in batches and knead briefly to form a very soft dough.
On a floured work surface, divide the dough into four equal pieces, roll each piece of dough in flour, and roll each piece out thinly on a sheet of baking paper into a rectangle about 30 cm x 38 cm (about the size of a baking sheet).
Also roll out the leftover dough thinly.
Bake the four thin cake layers one after the other in the preheated oven at 180 °C top and bottom heat for about 5 minutes each until they turn a light golden brown color.
While each cake layer is still warm, carefully cut it into two equal parts. Let the 8 cake layers you got now cool down.
Bake also the leftover dough, let it cool and crumble it finely.