Preheat the oven to 400° F. Have ready an enameled cast-iron Dutch oven or a baking sheet. Line the pot or the baking sheet with parchment paper. Have a floured surface ready for a quick knead on the dough, and a bench scraper if you have one.
Stir together in a large bowl the Irish whole meal flour, all-purpose flour, sugar baking powder, baking soda, and salt. Pour in most of the buttermilk and stir it into the dry ingredients. If the mixture still seems very dry, stir in the rest of the buttermilk.
Turn out the contents of the bowl onto the floured surface - the dough will still have some dry flour visible. Give the dough just a few quick kneads to pull it together. (You don't want to over-knead this bread as it will make it tough once baked.) Quickly shape it into a ball and place the dough into the pot or on the baking sheet.
Place the pot or baking sheet in the oven and bake for 10 minutes. Reduce the temperature to 375° F and bake the bread for another 40-45 minutes. The bread should be risen and browned, and sound hollow when tapped on the bottom.
Remove the bread to a cooling rack and let it cool for at least 30 minutes before slicing it. Serve slices of the bread with butter and jam. Tightly wrap leftover bread and use it within 2-3 days.