In a large bowl, whisk together flour, sugar, baking soda, baking powder and salt. Add in buttermilk and stir with a spoon or spatula until the dough starts to come together. Add in basil and mozzarella and continue to mix the dough until the dough is well combined.
Turn dough out onto a lightly floured surface and knead for about 1 minute, to smooth the dough and shape into a ball.
Place dough ball onto a baking sheet lined with parchment paper. Brush with 1 Tbsp. buttermilk. Using a sharp knife, cut a large X in the top of the dough.
Bake in a preheated 400-degree oven for about 26-30 minutes, until bread is golden.
Transfer bread to a wire rack and allow to cool completely before slicing.