Preheat the oven to 350°F (177°C). Lightly butter a 10-12 inch oven-safe skillet. Alternatively, you can use a 10-inch springform pan. 9-inch will be a little too small.

Whisk the flour, cornmeal, baking powder, baking soda, and salt together. Set aside.

Using a handheld or stand mixer fitted with a paddle attachment, beat the butter and brown sugar together on high speed until smooth and creamy, about 2 minutes. Scrape down the sides and up the bottom of the bowl with a silicone spatula as needed. Add the eggs and vanilla, then beat on medium-high speed until combined. Scrape down the sides and up the bottom of the bowl as needed. With the mixer on low speed, add the dry ingredients until just incorporated. With the mixer still running on low, slowly pour in the buttermilk until combined. Do not overmix. You may need to whisk it all by hand to make sure there are no lumps at the bottom of the bowl. Finally, fold in the fruit. The batter will be slightly thick. Spread into prepared skillet. Sprinkle with coarse sugar, if desired (and an extra blackberry or two!).

Bake the cake for 30-35 minutes or until a toothpick inserted in the center comes out clean. If baking in a 12-inch skillet, the cake shouldn’t take longer than 30 minutes since it will be thinner.

Remove from the oven and allow to slightly cool on a wire rack before icing and serving.

Slice the butter up into pieces and place in a light-colored skillet. (Light colored helps you determine when the butter begins browning.) Melt the butter over medium heat, stirring occasionally. Once melted, the butter will begin to foam. Keep stirring occasionally. After 5-6 minutes, the butter will begin browning—you’ll notice lightly browned specks begin to form at the bottom of the pan and it will have a nutty aroma. You can see a visual in my How to Brown Butter post. Once browned, remove from heat immediately and cool for 5 minutes. The butter will eventually solidify, so don’t let it sit too long. After 5 minutes, whisk in the rest of the icing ingredients until smooth. Add more confectioners’ sugar for a thicker texture, if desired. Likewise, add more milk to thin out if needed.

Drizzle over cornmeal cake. Slice and serve warm or you can wait until it’s full cool to room temperature. Cover leftover cake tightly and store in the refrigerator for up to 5 days.