Preheat oven to 375 degrees F (190 degrees C). Grease an 8-inch square pan.

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Beat butter and sugar together in a bowl until creamy. Add eggs; beat until combined. Stir in cornmeal.

Sift flour, baking powder, and salt together in a separate bowl. Stir flour mixture, alternating with milk, into butter mixture until well combined. Pour batter into prepared pan.

Bake in the preheated oven until a toothpick inserted in the center of the bread comes out clean, 30 to 35 minutes.