Preheat your oven to 350°. Generously butter a 9" springform pan. Add about two tablespoons of polenta into the pan and turn the pan to coat in a thin layer of polenta, Shake out and discard the excess polenta in the pan.
In a small sauce pan add the honey and 1/2 tablespoon of butter. Once the butter has melted and the honey has thinned (do not bring to a boil) pour over the blackberries and stir to coat.
To a medium-sized bowl add in the flour, polenta, salt, baking soda and powder, whisk to combine.
In the bowl of your stand mixer add the two sticks of butter, 1 cup cane sugar and the lemon zest. Blend on medium speed until light and fluffy.
Add in the dry ingredients. Mix until incorporated and crumbly.
Measure 1/4 cup of buttermilk into a liquid measuring cup, crack in the three eggs and lightly beat.
Remove the bowl from your mixer and pour in the buttermilk/egg mixture. Using a rubber spatula, stir by hand until just combined.
Spoon the cake batter into the prepared springform pan. Dot the cake batter with the honeyed blackberries. Pour the remaining honey over top of the cake and berries.
Bake for 45-50 minutes on the center rack in your oven. Once a cake tester comes out clean or with only a few crumbs, the cake is done.
Let cool for 10 to 15 minutes before releasing the spring. Let cool slightly before cutting and serving. This cake is excellent still warm.