Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper and set aside.

Whisk flour, sugar, baking powder, baking soda, and salt together in a large bowl. Cut in butter using a pastry blender or fork until mixture resembles coarse crumbs. Pour in 1 cup buttermilk, and stir just until combined. Fold in strawberries and basil.

Dust a work surface lightly with flour and divide dough in 1/2. Shape each portion into a 3/4-inch-thick circle; cut each into 8 wedges. Place the wedges onto the prepared baking sheet, about 2 inches apart. Brush tops of scones with 2 tablespoons buttermilk and lightly sprinkle with brown sugar.

Bake in the preheated oven until golden brown, 15 to 20 minutes. Serve warm or at room temperature.