Preheat your oven to 350°F (175°C) and grease a 9-inch round baking pan.

In a large mixing bowl, whisk together the gluten-free all-purpose flour, granulated sugar, baking powder, salt, and ground cinnamon.

In a separate bowl, combine the melted butter, egg, and milk. Mix well until fully blended.

Pour the wet mixture into the dry ingredients and stir gently until just combined.

For the filling, mix the brown sugar and ground cinnamon in a small bowl and set aside.

On a lightly floured surface, roll the dough into a rectangle about 1/4 inch thick. Spread the softened butter over the surface of the dough and sprinkle the cinnamon and brown sugar mixture over it.

Starting from one long side, roll the dough into a tight log and slice into 12 equal pieces. Place in the prepared baking pan.

Bake for 25-30 minutes until golden brown.

While the rolls are baking, prepare the icing by mixing powdered sugar with 1 tablespoon of milk until smooth.

Once the rolls are done baking, let them cool for a few minutes and drizzle the icing over the warm rolls.