Preheat the oven to 400 degrees F. Lightly oil a baking sheet or line with parchment paper.
Sift the flours, baking soda and salt together in a bowl. Stir in the Cheddar and chopped rosemary. Make a well in the middle. Add the buttermilk and, using a fork, mix until just combined. This will give you a soft, sticky dough, which makes a nice moist loaf. With floured hands, divide the dough into 4, scrape each one onto the prepared baking sheet and pat into a light round. Using a chef's knife, deeply score each soda bread with a cross on top (this will allow the heat to penetrate the center of the dough).
Bake until the breads are dark golden all over and sound hollow when you tap the bottoms, about 30 minutes.