Stir together brown sugar and cinnamon in a bowl. Set aside.
Whisk together flour, baking powder, salt, and sugar in a bowl.
Make a well in the center then add in egg, oil, and milk. Mix to combine.
Swirl in the cinnamon sugar.
Divide the batter into a lined muffin tin.
Bake for 25-30 minutes at 350F.
Blend together cream cheese, butter, vanilla, and powdered sugar until smooth.
Take the muffins out of the oven and leave to cool.
Drizzle prepared icing on top.