In a large bowl, combine the gluten free flour, baking powder, salt and 3 tablespoons of melted butter. Add ¼ cup sugar, 1 ¼ cups milk, and 1 egg. Combine until a dough forms.
Place the dough on a surface sprinkled with gluten free flour. Roll the dough out into a rectangle. Spread the butter onto the dough.
Combine the remaining ½ cup sugar and 2 teaspoons cinnamon in a small bowl and sprinkle evenly across the dough. Roll the dough up. Slice the dough every ½ inch.
Place the rolls in a cake pan or pie plate sprayed with cooking spray.
Place in the oven and bake for 20-25 minutes.
While the cinnamon rolls are baking, prepare the icing by whisking the remaining ¼ cup milk and 1 cup powdered sugar together in a small bowl.
Drizzle the icing over the cinnamon rolls when they come out of the oven.