Mix the eggs and sugar well into a creamy white mixture.
Then mix the flour, cinnamon, vanilla sugar and baking powder together. Mix in well. Add the melted butter / oil as well as the finely grated carrots and the orange peel. Mix everything again. Put the dough in a greased round dish and let the cake bake for 45-55 minutes. If the cake turns too brown, you may want to put aluminum foil over it. Take the cake out of the oven and pan and let it cool on a baking rack. If necessary, put a towel over it and only start glazing when the cake has cooled down completely.
Mix together the ingredients for the icing. Divide the cake crosswise and apply half of the icing to the bottom half. Put the top part of the cake back on top and coat the cake completely with the rest of the icing.
Annotation:
This is a recipe used by most Norwegians. I myself prefer a little less sugar, as the carrots themselves add a certain sweetness. Just try it yourself, but 2 - 2.5 dl of sugar are usually sufficient for the dough. You can also save a little on the icing sugar for the glaze.