Preheat oven to 375°F. Line a standard 12-cup muffin pan with paper liners; set aside.
In a large bowl, whisk together flour, sugar, oats (if using), baking powder, cinnamon, salt, and nutmeg.
In a medium bowl, whisk together buttermilk (or milk), melted butter, oil, eggs, and vanilla extract.
Add the wet ingredients to the dry ingredients. Stir just until combined, being careful not to over-mix. The batter may be lumpy, which is fine.
Fold in the blackberries.
Divide batter evenly among the prepared muffin cups, filling each cup almost to the top. Sprinkle coarse sugar on top, if desired.
Bake for 17-20 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs attached.
Transfer muffins to a wire rack to cool. Serve warm or at room temperature.