Preheat the oven to 425°F. Lightly grease a large cast-iron skillet with cooking spray, or line a large baking sheet with parchment paper for an alternative option.

In a large mixing bowl, whisk together the whole wheat flour, all-purpose flour, sugar, baking soda, and salt until evenly combined. Add in the cubed butter and use your fingertips to rub it into the dry ingredients until the mixture resembles coarse crumbs with pea-sized and slightly larger pieces scattered throughout.

In a separate bowl, whisk the egg with the buttermilk. Create a well in the center of the flour mixture and pour in the wet ingredients. Starting from the center and working outward, stir the mixture with a wooden spoon until the dough becomes too stiff to mix further.

Turn the dough out onto a lightly floured surface. Dust your hands with flour and shape the dough into a rough ball, kneading gently just until all the dry patches disappear—about 30 seconds. Take care not to over-knead to maintain a tender crumb.

Place the shaped dough onto the prepared skillet or baking sheet. Using a sharp knife, score a deep X, about 1/2 inch, into the top of the dough to help it expand while baking.

Bake for 15 minutes, then reduce the oven temperature to 400°F and continue baking for another 30 to 35 minutes, or until the crust is golden and the base sounds hollow when tapped.

Let the bread rest for 5 to 10 minutes, then transfer to a wire rack. Slice and serve warm, at room temperature, or toasted to your liking.