Preheat oven to 350 degrees F with baking rack in center of oven.
Grease a 9-inch springform pan with nonstick cooking spray.
In a large bowl, beat together eggs and sugar until frothy. Add in oil, milk, baking powder, vanilla, and salt until combined well.
Add in flour and mix just until the batter is combined. Fold in grated carrots.
Pour cake batter in prepared springform pan. Bake for 50-60 minutes or until inserted toothpick comes out clean. Allow to cool 15 minutes before loosing and removing collar.
Once cake is completely cooled, dust with confectioners sugar before slicing and serving.