Whisk eggs and sugar in a bowl until pale and slightly thickened.
Stream in melted butter, then whisk in milk and vanilla until smooth.
Combine flour, cardamom, and salt in a separate bowl. Fold into wet ingredients just until no dry spots remain.
Let the batter rest 10 minutes while you heat the krumkake iron to medium and lightly grease it.
Spoon about 1 tbsp batter onto the iron. Close and cook until golden, 30–45 seconds, adjusting heat as needed.
Lift the wafer and immediately roll it around a cone form. Hold a few seconds to set, then place on a rack.
Repeat with remaining batter, greasing the iron lightly as needed. Dust cooled cookies with powdered sugar.