Preheat the oven to 375°F (190°C) and line a muffin tin with paper liners.
In a large bowl, combine the flour, oats, brown sugar, baking powder, baking soda, and salt.
In another bowl, whisk together the eggs, buttermilk, vegetable oil, lemon zest, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir just until combined. Gently fold in the blackberries.
Spoon the batter into the prepared muffin cups, filling each about three-quarters full. Press a few extra blackberries on top of each muffin if desired, then sprinkle with coarse sugar.
Bake for 20 to 22 minutes, or until a toothpick inserted in the center comes out clean. Remove the muffins from the pan right away and cool on a wire rack.
While the muffins bake, make the glaze by stirring together the confectioners’ sugar, lemon zest and juice in a small bowl until smooth.
Once the muffins are completely cooled, spoon the glaze over the tops and let it soak in. Sprinkle with more coarse sugar while the glaze is still wet, if desired.
