Preheat your oven to 375°F (190°C). Line a muffin tin with paper liners or grease it with cooking spray.
In a large bowl, combine the flour, sugar, baking powder, baking soda, and salt. Whisk together until well mixed.
In another bowl, whisk together the egg, buttermilk, vegetable oil, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Be careful not to overmix; a few lumps are okay.
Gently fold in the mulberries, being cautious not to break them up too much.
Divide the batter evenly among the muffin cups, filling each about ¾ full.
Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.