Preheat oven to 400 degrees F (200 C). Lightly grease a standard muffin pan, and set aside.
In a medium bowl, whisk together the flours, sugar, baking powder, caraway seeds, salt, and baking soda.
1 and 1/2 cups (180 grams) all-purpose flour, 3/4 cup (85 grams) white whole wheat flour, 1/3 cup (67 grams) granulated sugar, 2 teaspoons baking powder, 1 teaspoon caraway seeds, 1/2 teaspoon table salt, 1/4 teaspoon baking soda
In a separate large bowl, whisk together the egg, buttermilk, and melted butter.
1 large egg, 1 cup (240 ml) buttermilk, 6 Tablespoons (85 grams) butter
Pour the wet ingredients into the dry, and stir gently to combine. Do not overmix; stop as soon as the batter is evenly moistened.
Divide batter evenly among the prepared muffin wells, filling each about 3/4 full. The batter will be stiff and form small mounds in the wells. Sprinkle a small amount of additional white sugar on top of each muffin, if desired.
Bake for 20-24 minutes, until a toothpick or cake tester inserted into the center of a muffin comes out clean. Remove pan from the oven, and gently tip the muffins in the pan; this prevents the bottoms from getting soggy. After 5-10 minutes, remove muffins to cool directly on a wire rack. Serve slightly warm, with butter.