Heat oven to 400° F. Line a 12-cup muffin tin with paper liners or coat it with cooking spray, vegetable oil, or butter.
In a medium bowl, combine 1 3/4 cups of the flour, 1/2 cup of the sugar, the baking powder, and salt. Add the butter and combine. In a second bowl, whisk together the milk, egg, and vanilla. Gradually add the milk mixture to the flour mixture and stir until just combined; the batter will be lumpy. Toss the berries with the remaining flour in a bowl. Gently fold the berry mixture into the batter.
Fill each muffin cup 3/4 full. Sprinkle the batter with the remaining sugar. Bake for 17 to 20 minutes or until a toothpick inserted into the center of a muffin comes out clean. Transfer pan to a wire rack to cool for 10 minutes. Serve warm.