Preheat your oven to 375°F (190°C). In a large mixing bowl, combine all-purpose flour, bread flour, baking powder, baking soda, and salt. Whisk to ensure even distribution of dry ingredients. In a separate bowl, whisk eggs, then add grape-seed oil and buttermilk. Mix well to create the wet ingredients.

Pour the wet mixture into the dry ingredients. Stir gently with a spatula or wooden spoon until just combined. Then, fold in the cubed mozzarella, chopped basil, and sun-dried tomatoes, distributing them evenly throughout the dough. Do not overmix; a shaggy dough is perfect.

Transfer the dough into a greased or parchment-lined loaf pan. Spread it out evenly. Optionally, sprinkle extra chopped basil or sun-dried tomatoes on top for visual appeal and flavor. Place the pan in the preheated oven and bake for about 40-45 minutes, or until the crust is golden and a toothpick inserted into the center comes out clean.

Remove the bread from the oven and let it cool in the pan for 10 minutes. Then, transfer to a wire rack and allow it to cool slightly. This resting period ensures the cheese sets, and the flavors meld beautifully. Slice while warm or at room temperature, and enjoy the fragrant, savory, and melt-in-your-mouth goodness.