Combine the blackberries, sugar, lemon zest, rosewater, and cardamom in a bowl. Set aside.
Preheat the oven to 350° F. Grease and flour a 10" deep dish pie plate, 10" x 10" pan, or 11" pie plate, and set aside.
Cream the butter with the sugar, vanilla, and salt in the bowl of a standing mixer fitted with the paddle attachment until light, about 2-3 minutes. Add the eggs, one at a time, waiting until each egg is completely mixed in before adding the next. You may need to scrape the bowl in between adding the eggs, particularly after the first one.
Whisk the flours and baking powder together to thoroughly distribute the baking powder through the flours. Even though this is a buckle, it's nice to have an even buckling, so to speak. Fold the flour mixture into the batter in thirds using a spatula until combined. Pour in the buttermilk and continue folding until no streaks remain.
Pour the batter into the prepared pan and smooth out the surface. Top the cornbread evenly with the berries. By now, there should be some juices in the berry bowl - make sure you add those too! The berries should cover the entire cake.
Sprinkle the Oat Crumb Topping evenly over the fruit, and bake until a pick comes out clean, about 1 hour to 1 hour and 15 minutes. Because of all the berries, it's good to test the cake in a few areas. This cake is fantastic served warm or cold, but warm is just a little better. And don't forget a scoop of ice cream.