Preheat oven to 425 degrees Fahrenheit and lightly grease a 10" cast iron skillet with cooking spray (or line a baking sheet with parchment paper).
In a large bowl, whisk the flour, whole wheat flour, sugar, baking soda, and salt together until well mixed.
Add butter and using your hands, mix until pea-sized pieces form.
In a smaller bowl, whisk the egg and buttermilk together until smooth.
Make a well in the center of the flour and pour egg mixture into the center. Mix with a wooden spoon (or rubber spatula) until the dough is too stiff to stir.
Turn dough out onto a lightly floured surface and form into a ball. Knead dough until no streaks of flour are seen (about 30 seconds). Do not overwork the tough or the bread will be tough.
Transfer the dough ball to the prepared skilled (or baking sheet) and using a sharp knife score an "X" on the top of the loaf, about 1/2 inch deep.
Bake bread for 15 minutes at 425 degrees, then reduce heat to 400 degrees and continue baking for 30-35 minutes, until the bread is golden brown.
Let bread cool for several minutes in the pan prior to transferring to a wire rack to cool completely. Serve warm or toasted with butter.