Preheat oven to 350 degrees F (175 degrees C). Grease a 9x9-inch 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. Add the flour mixture in three parts, alternating with the whipping cream, mixing until combined. Pour the batter into the prepared pan.
Bake in preheated oven until a toothpick inserted near the center comes out clean, 30 to 40 minutes.
