Preheat oven to 400°. Grease a 12-cup muffin pan. In a mixing bowl, combine flours, baking powder, salt, and cinnamon, and whisk together. In a second mixing bowl, combine melted butter, egg, brown sugar, and milk, and blend until smooth.
Add dry ingredients to wet, stirring to combine. Stir in the carrot and cranberries. Fill muffin cups and bake until golden brown on top, about 20 minutes.