In a bowl, whisk together the flour, sugar, salt, and baking powder.
In another bowl, whisk the eggs, then add the milk, melted butter, and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined and the batter is smooth.
Heat an aebelskiver pan over medium heat and grease each well with a little butter.
Pour a small amount of batter into each well.
As the edges begin to set, use a toothpick or fork to rotate the aebelskivers, so they cook evenly on all sides.
Cook until golden brown all over, then remove from the pan.
Serve dusted with powdered sugar, alongside jam or honey.
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