Adjust the oven rack to the middle position, pre-heat the oven to 350ºF (180ºC) and line a 9-inch (23cm) square baking pan with parchment/baking paper.

In a large bowl, whisk together the sugar, melted butter, oil, eggs, yoghurt, milk and vanilla until well combined and smooth.

In a separate bowl, whisk together the gluten free flour blend, baking powder, xanthan gum and salt.

Add the dry ingredients to the wet and whisk well until you get a smooth, fairly loose cake batter with no flour clumps.

Pour the vanilla cake batter into the lined baking pan and smooth it out into an even layer.

Mix together the light brown sugar, cinnamon and gluten free flour blend until well combined, then add the melted butter and mix well until you get a loose, paste-like consistency.

Drop small dollops of the cinnamon-sugar filling all over the cake batter, and use a skewer or the end of a knife to gently swirl it around.

Bake the cake at 350ºF (180ºC) for about 25-28 minutes or until it's golden brown on top and an inserted toothpick or cake tester comes out clean.

Allow the cake to cool in the baking pan for about 20 minutes while you prepare the icing.

In a bowl, mix together the cream cheese, powdered/icing sugar and vanilla until smooth and no clumps remain.

Add the milk and mix until smooth. The icing should be runny but not too thin.

Pour the icing over the warm cake and use the back of a spoon to spread it around.

Slice and serve. You can enjoy the cake either warm or cooled completely to room temperature.