"Abel-sheever" or "Eebel-sheever"
First and foremost, you MUST have a proper abelskiver pan to make these. Mine is cast iron--I think they all are. If you don't have the right pan, don't bother trying to make them. It won't work. If you need one, you can get them here.
OK, so now that we have that out of the way, I've noticed that several countries seem to have their own variations on pancakes...there are crepes in france and johnny cakes in the southern USA, and abelskivers are the Scandinavian version. Like crepes and german pancakes, they are heavy on the eggs, and make a hearty breakfast if you can eat them slowly enough to feel how full you're getting!
I tried the recipe that came with my pan, but I prefer this one which I copied out here (I figured I should give the source link too)
Hubby says that in Denmark they actually make them more spherical--they pull each one up the side of the depression and cook it in 3-4 steps rather than just flipping it over and cooking it in 2 steps like I do. One day I may get up the energy to try that, but for now I just flip them over and they are puffy but not really balls. It's faster. ☺
4 eggs, separated
1 tablespoon sugar
2 cups cake flour
1 teaspoon salt
1 teaspoon baking powder
1/4 cup melted shortening
Scant 2 cups milk
Beat egg yolks; beat in sugar. Combine dry ingredients. Add alternately with shortening and milk. Beat egg whites until stiff, but not dry. Fold into batter. Grease an Abelskiver pan (I put about 1/4tsp of butter in each depression). Heat until smoking. Fill depressions about half full.
(I use a smallish spoon. There is definitely a learning curve to it, and I botched several batches before getting it straight...having a well-greased pan helps a lot.) Cook other side until cooked through. Regrease pan between batches (I use about 1/2tsp butter spread between the 7 depressions--just a tiny dot in each, although once you've developed a good seasoning on your cast iron then you'll only need to grease every 4th or 5th batch).
Serve warm with applesauce or sprinkled with sugar. We also like them with fruit + powdered sugar, fruit + whipped cream, or the boys like them with plain old maple syrup.
As with all my cast iron, I use only saturated fats to grease my abelskiver pan (in this case butter) because they put in a good seasoning (nonstick surface) and unsaturated fats will just break down. I also never wash it with soap--cast iron is porous and the soap will get into the pan and stay there (and then get into our food). I take the pan while it is still hot, and wash it with straight hot water from the tap. I have a (never-touches-soap) long-handled scrubby brush that I use if there is stuff stuck to the inside, but often a good rinse just gets everything nice and clean. Then just make sure the pan is fully dry before putting it away so that it will not rust. ☺