Even though I have many Danish cookbooks, I´m not quite sure which cakes you mean, because they are without doubt called something entirely different in Danish. But here are two recipes that might be worth trying - they are Icelandic but most of our old cookie recipes come from Denmark anyway. I always bake both types for Christmas.

Kartöflumjölskökur
(Potato flour cookies)

4 oz potato flour
4 oz flour
4 oz sugar
1/2 tsp hartshorn (ammonium carbonate ?)
4 oz butter
1 egg
coarse sugar (or crushed sugar cubes)

Mix potato flour, flour, sugar and hartshorn and rub the butter into this mixture until well combined. Make a well in the middle. Beat the egg lightly and pour half into the well. Mix gradually with dry ingredients and knead until smooth. Make a ball of dough, wrap it and refrigerate for at least two hours. Take bits of dough (slightly less than walnut-size), roll into balls and flatten them somewhat. Dip one side into remaining egg and then into sugar. Bake at 375 for 8-10 minutes, or until faintly golden. Sometimes the cookies are not dipped in egg and sugar, but left as they are or drippled with melted chocolate when cold.

Spesíur

8 oz plain flour
7 oz butter
2 1/2 oz confectioners´ sugar
1 small egg
coarse sugar

Cut cold butter in small pieces and rub into flour. Sift sugar over and knead very ligthly (the less the better). Roll into two lenghts, 1 1/4 - 1 1/2 inch thick. Cover and refrigerate for at least two hours. Brush with egg and roll in sugar. Cut into thin slices and bake at 400 for 5-6 minutes, or until faintly golden. Sometimes chopped or ground almonds, chopped chocolate, nougat or raisins is added to the dough.