Preheat oven to 375°F (190°C) and line a standard 12-cup muffin tin with paper liners.
In a large mixing bowl, whisk together the gluten-free flour blend, granulated sugar, baking powder, baking soda, and salt until uniform.
In a separate medium bowl, whisk the sour cream, eggs, melted butter, and vanilla extract until a smooth emulsion is formed.
Create a well in the center of the dry ingredients and pour in the wet mixture.
Using a silicone spatula, gently fold the ingredients together until just combined; do not overmix as this can affect the rise.
Gently fold in the blackberries, taking care not to crush them and dye the batter.
Portion the batter evenly into the 12 prepared muffin cups, filling each approximately 3/4 full.
Sprinkle the top of each muffin with a small amount of turbinado sugar for texture.
Bake for 22 to 25 minutes, or until the tops are golden brown and a toothpick inserted into the center comes out clean.
Cool the muffins in the tin for 5 minutes before transferring to a wire cooling rack to reach room temperature.