Preheat oven to 180 degrees C. Grease one 20cm square pan.
Beat eggs in a small bowl until very thick. Add the sugar and the vanilla, beating well.
Combine the flour, baking powder and salt. In three parts add the flour mixture alternately with the cream to the egg mixture, beginning and ending with the flour mixture. Pour the batter into the prepared pan.
Bake for 30 to 40 minutes or until a toothpick inserted near the centre comes out clean.