Preheat oven to 350 degrees. With a mixer, beat the eggs with the sugar until slightly thickened and light in color, about 5;7 minutes. The mixture should almost double in size. The eggs work as your leavening agent in this recipe, so do not skip this step. The mixture should form a ribbon when you lift the beaters out of the bowl.
Add the butter and vanilla; mix two more minutes. Stir in the flour until just combined. This will be a very thick batter. Add the berries and stir to mix throughout.
Transfer the batter to a buttered 9x13 pan. Use your hands to press it into an even layer.
Bake for 40-50 minutes or until very lightly browned and a toothpick inserted near the center of the cake comes out clean. Let cool and cut into pieces.