Preheat oven to 375ºF. Line a baking sheet with parchment paper.
Combine all-purpose flour, whole wheat flour, baking soda, salt and ginger in a large bowl; mix well.
In a small bowl, combine buttermilk and molasses; mix well. Stir buttermilk mixture into the flour mixture. Add additional buttermilk by tablespoonfuls if needed to make dry, rough dough. Transfer dough to floured surface; knead 8 to 10 times or just until smooth (do not overknead). Shape dough into a round loaf about 1-1/2" thick. Transfer to prepared baking sheet.
Use floured knife to cut halfway through dough, scoring into quarters (called "farls" in Ireland). Sprinkle top of dough with additional flour, if desired.
Bake about 35 minutes or until bread sounds hollow when tapped. Remove to a wire rack to cool slightly. Serve warm. Note: Bread can be sliced or pulled apart into farls.