Prep: Preheat oven to 400°F. Line a 12-cup muffin pan with muffin liners and set aside.
Mix dry ingredients: In a medium bowl, stir together flour, oats, sugar, baking powder, and salt. Set aside.
Mix wet ingredients: In a large mixing bowl, mash the bananas with the back of a fork until very mushy. Add the oil, egg, buttermilk, and vanilla extract and whisk together until combined.
Fold together batter: Add the flour mixture to the wet mixture and fold together with a spatula until just barely combined.
Fold blackberries into batter: In a medium bowl, toss the chopped blackberries in a tablespoon of flour to soak up any excess liquid. Add the coated blackberries to the batter and gently fold them together just until the blackberries are distributed evenly throughout the batter.
Fill muffin pan: Use two spoons or a cookie scooper to fill the muffin liners completely full with batter. Sprinkle sugar on top of each muffin.
Bake: Bake muffins for about 23-25 minutes or until the tops are lightly golden brown and a toothpick inserted in the middle comes out clean. Let the muffins cool in the pan for about 15 minutes before transferring them to a wire rack to cool or enjoy them warm.