Preheat the oven to 375 degrees F (191 degrees C). Line a cookie sheet with parchment paper.
Mix flours, rolled oats, sugar, baking powder, baking soda, and salt in a medium bowl. Mix buttermilk and melted butter together in a small bowl.
Make a small well in the flour mixture and pour in the buttermilk-butter mixture. Stir together with a wooden spoon until well combined.
Turn the dough out on a generously floured surface and knead into a smooth, round loaf. Place on the cookie sheet and cut a shallow X into the top of the dough.
Bake in the preheated oven until top is golden brown, about 1 hour. Carefully tap the bottom of the loaf; it should sound hollow. Cool on a baking rack for at least 30 minutes before slicing.