Preheat the Oven to 350 degrees Fahrenheit
Butter a Gugelhopf pan (My Oma would use the butter wrapper, and rub it in the grooves)
Combine the Eggs, Powdered Sugar, Vanilla Extract and pinch of salt in a mixer. Beat until thick and a bit foamy. Don't skimp on this step. (I let the machine work for 5 minutes)
Add the Eierlikör, beat 2 minutes
Add the Oil, beat 2 more minutes
Combine all the dry ingredients (flour, cornstarch and baking powder), then carefully fold them into the batter.
Pour the batter into the prepared Gugelhopf form. It will look fairly runny.
Bake 60 minutes... check if it's done by sticking in a toothpick. If the toothpick comes out clean, take it out. If there is still wet dough on the toothpick, bake a little longer.
Let the baked cake sit on a rack for 10 minutes to set.
Turn the cake out of the pan, and cool completely.