Preheat oven to 350F and grease a 9x13 inch baking pan.
In a large bowl, mix the gluten free all-purpose flour, granulated sugar, baking powder, milk, eggs, and melted butter until a smooth batter forms. Pour into the prepared pan.
In a smaller bowl, mix the softened butter, brown sugar, and ground cinnamon until it forms a thick paste.
Drop spoonfuls of the cinnamon paste randomly over the unbaked cake batter.
Use a butter knife to swirl the cinnamon mixture through the cake batter, creating a marble effect. Bake for 25-30 minutes until the cake is springy.
While the cake bakes, whisk the powdered sugar and milk together in a small bowl until a smooth, thick icing forms.
Drizzle the sweet icing generously over the warm cake. Let it set slightly before slicing.