First, melt the butter and set it aside.
Mix together the almond or cashew milk with apple cider vinegar and set it aside to curdle while you continue with the rest of the ingredients.
Next, separate the egg whites from the yolks. Place the egg yolks in a large mixing bowl and the egg whites in a smaller bowl with high sides. Use a hand mixer to beat the egg whites until stiff peaks form. Set both bowls aside.
In a medium sized bowl, add the gluten-free flour, baking powder, baking soda, salt, and stir together. Set off to the side.
Then in the bowl with the egg yolks, stir in the cooled butter and the milk and vinegar mixture. Then stir in the dry ingredients until the batter is smooth.
Use a rubber spatula / scraper to add in the beaten egg whites. Gently fold in the whites into the batter until it is fluffier in texture.
Heat the cast iron aebleskiver skillet on the stove over medium heat. Melt about 1 tablespoon of butter and use a pastry brush to apply a small amount of butter to each hole on the heated skillet. Then use a smaller spoon to fill each hole to the rim with batter. Cook for 3 minutes before inserting a metal or wooden skewer to flip them over and cook for another 3 minutes or until fully cooked.
Continue applying butter on the skillet in between each batch. Place cooked aebleskivers in a bowl covered with a towel or foil to keep warm. Serve them warm with jam, powdered sugar, or whipped cream and berries.