Prepare Dry Ingredients: In a mixing bowl, combine the flour, sugar, baking powder, and salt. Stir well.
Mix Wet Ingredients: In a separate bowl, whisk together the eggs, sour cream, milk, and melted butter until smooth.
Combine Wet and Dry Ingredients: Pour the wet ingredients into the dry ingredients and stir gently until just combined. The batter should be thick but still pourable.
Heat the Aebleskiver Pan: Preheat the pan over medium heat and lightly grease it with butter or cooking spray.
Cook the Aebleskivers: Using a spoon or ladle, pour the batter into each well of the pan, filling about three-quarters full. Cook for about 2-3 minutes until the edges start to set and the bottom turns golden brown.
Flip and Finish Cooking: Using a skewer or chopstick, carefully flip each aebleskiver over and cook the other side for another 2-3 minutes until golden brown and cooked through.
Serve: Remove the aebleskivers from the pan and serve immediately with your preferred toppings like extra sour cream, syrup, or fresh fruit.