Combine flour, baking powder, sugar, salt, and cardamom. Add cold butter cut into pieces and eggs. Mix for about 5 minutes until a smooth dough forms. Cover and chill for at least 2 hours.
While dough chills, combine plum jam and rum in a saucepan. Bring to a boil over medium heat and simmer for 10-15 minutes, stirring often, until thick. Set aside to cool.
Roll out the chilled dough on a floured surface. Cut out circles.
Place about 1/2 teaspoon jam on each circle. Fold in half to form a semi-circle. Press the edges lightly with a fork to seal.
Brush each cookie with milk.
Place on a baking sheet and bake in a preheated oven at 160-180°C (320-356°F) for 12-15 minutes until lightly golden.
Cool on the baking sheet for 10 minutes, then transfer to a wire rack to cool completely.
Dust half of the cookies with cocoa powder and the other half with powdered sugar.