Preheat oven to 350°F and grease an 8×4-inch loaf pan.
In a large bowl, whisk together all-purpose flour, bread flour, baking powder, baking soda, and salt.
Add chopped basil, mozzarella cubes, and sun-dried tomatoes to the dry ingredients and toss to coat evenly.
In a separate bowl, whisk together eggs, oil, and buttermilk.
Pour the wet ingredients into the dry mixture and stir gently with a wooden spoon until just combined. The dough will be sticky.
Transfer the batter to the prepared loaf pan and spread evenly.
Bake for 40–45 minutes, or until a toothpick inserted in the center comes out mostly clean.
Cool slightly before slicing and serving.