In a large bowl, whisk together the eggs and sugar. Mix in the buttermilk, vanilla and oil. Stir in the flour, baking soda, baking powder and salt until just combined.
Pour 3-4 tablespoons oil in a small cup and keep near the stove. You'll need a pastry brush or paper towel to rub oil into the pan between batches.
Preheat an ebelskiver pan over medium heat for 4-5 minutes until hot (the batter should sizzle when poured into the pan - but take care it isn't so hot to burn the ebelskivers). Brush each cup with a tiny bit of oil.
Pour enough batter into each cup to fill about 3/4 of the way. If you are planning on adding a filling (like fruit/jam, etc.) don't fill quite as full. Let the ebelskivers cook for a minute or so until tiny bubbles begin to show on the surface and the edges look like they are setting a bit. Add any filling to the center of the batter at this point and top with a tiny bit of batter to cover.
Using a knitting needle or other similar long, thin tool, push the tip into the middle of the batter to the bottom of the cup and gently lift the ebelskiver so that it turns and the cooked part is lifted out of the pan. The uncooked batter will run into the bottom of the cup.
Let the ebelskiver cook a bit more (it will depend on how hot your pan is - don't let them burn!) and turn again, slightly twisting so the seam from the first turn lifts out of the cup, with the needle so that it begins to form a ball shape (see the step-by-step pictures below). If the cooking process seems confusing, just simply keep turning the ebelskiver so it doesn't burn and so that it cooks evenly on each side.
Again, let it cook for a minute and then turn again so the opening is now on the bottom of the hot pan to cook all the way through.
I like to toss the cooked ebelskivers in a 9X13 pan and keep them in a warm oven (about 175 degrees or so) until they are all cooked. Serve warm with any variety of toppings: syrup, fruit and whipped cream, nutella, powdered sugar, jam. The options are endless!
Flour: I always use at least 1/2 white wheat flour (sometimes more like 3/4) instead of all white flour and they are still absolutely delicious. Ebelskiver Pan: it's super duper important if using a cast iron ebelskiver pan (like in my pictures) that it is well-seasoned. You can google how to season a cast iron pan - but proper seasoning will make all the difference in the world so that the ebelskivers don't stick.