1. Preheat oven to 375 degrees F. Line a 12-cup muffin pan with baking papers and set aside.
2. Stir flour, cornmeal, sugar, baking powder, and salt together in a medium bowl using a whisk. Set aside. Whisk eggs, buttermilk, butter, and vanilla together in a medium bowl. Fold egg mixture into dry ingredients using a rubber spatula, mixing just until batter forms but remains slightly lumpy. Fold in blackberries.
3. Divide batter among muffin cups, sprinkle with sugar, and bake on top shelf of oven until muffins are golden and a wooden toothpick inserted in center tests clean, about 20 minutes. Release muffins from tin and transfer to a cooling rack; serve warm.
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