Preheat oven to 350 degrees F (175 degrees C). Sprinkle cornmeal onto a baking sheet or spray with cooking spray.
Combine 1 1/2 cup all-purpose flour, whole wheat flour, oats, brown sugar, baking soda, and salt together in a large bowl. Cut butter into flour mixture using a pastry blender or your fingers until mixture resembles coarse crumbs.
Stir buttermilk into flour mixture using a fork just until dough is blended; knead 5 times in the bowl. Turn dough onto a floured surface; knead dough using floured hands 8 to 10 times; shape into a 6- to 8-inch loaf.
Place loaf on the prepared baking sheet and sprinkle about 1 teaspoon flour over loaf. Cut a long 'x' over the top of the loaf using a serrated knife.
Bake in the preheated oven until bread is golden, sounds hollow when top is tapped, and internal temperature is 190 degrees F (88 degrees C), 45 to 50 minutes.