Heat oven to 400 degrees F. Line 12 medium muffin cups with paper baking cups or grease bottoms only with shortening.
Mix brown sugar and cinnamon; set aside.
In a large bowl, beat milk, applesauce, oil, vanilla, and egg with fork or wire whisk. Stir in flour, granulated sugar, baking powder, and salt all at once just until flour is moistened (batter will be lumpy). Fold in raspberries and blueberries.
Divide batter evenly among muffin cups. Sprinkle brown sugar mixture evenly over tops of muffins.
Bake 20 to 25 minutes or until golden brown. Immediately remove from pan and place on wire rack. Serve warm.