In a large bowl, whisk together flour, sugar, baking powder, baking soda, and salt.
In another bowl, mix milk, egg, and melted butter. Pour wet ingredients into dry ingredients and stir until just combined.
In a small bowl, mix melted butter, brown sugar, and cinnamon for the swirl. Transfer to a piping bag or zip-top bag with a small corner cut off.
Heat a non-stick skillet over medium heat. Pour ¼ cup of batter onto the skillet. Pipe a swirl of the cinnamon mixture onto the pancake.
Cook until bubbles form on the surface, then flip and cook until golden brown. Repeat with remaining batter.
For the glaze, beat cream cheese until smooth. Add powdered sugar, vanilla, and milk, and mix until smooth.
Drizzle glaze over warm pancakes and serve.