Preheat over to 350 degrees farenheight.
Pre-butter an 8" round or square baking pan.
In a large mixing bowl, add gluten-free flour, salt, baking powder, cinnamon, and sugar. Mix thoroughly.
In the same mixing bowl, add milk, egg, vanilla extract, and melted butter. Mix until completely incorporated.
Pour batter into the baking pan.
Now make the cinnamon swirl. In a small mixing bowl add brown sugar, cinnamon, and melted butter. Mix thoroughly.
Slowly drizzle the cinnamon swirl over the batter.
With a knife, chopstick, or another similar tool, gently swirl the cinnamon mixture into the batter.
Place pan in the oven and cook for 26-28 minutes (if you are using a square pan, you may need to cook for even less time. I recommend checking the cake at 23 minutes and using a wooded toothpick to check if the middle is cooked through). The cake will also be cooling inside the pan so it is okay if it is just slightly under baked when removing from the over. As it cools in the hot pan it will continue to bake.
While the cake is baking, prepare the cinnamon glaze. Add powdered sugar, cinnamon, and milk to a bowl and mix thoroughly.
Once the cake is finished baking, remove from the oven and allow to cool for about 10 minutes.
Drizzle the cinnamon glaze over the cake and serve!