Preheat the oven to 350°F (175 °C). Butter and flour a tart pan (with removable bottom). Place the tart pan on a baking sheet.
Sift the flour, cornmeal, baking powder and salt into a medium bowl. Set aside for later
In a large bowl, cream the butter and the sugar. Add the egg and the vanilla and mix until well incorporated.
Add the dry ingredients to the batter, alternateing with the milk.
Pour the batter into the prepared pan, scatter the berries over top, and bake it for 45–50 minutes or until the middle is set and a cake tester inserted into the middle comes out clean.