Preheat oven to 190/170°C Fan. Grease and line an 8" (20cm) round cake tin.
Make the cinnamon filling by melting the butter. Add in the brown sugar, cinnamon and nutmeg. Mix until well combine and set aside.
Melt the butter, and set it aside to cool. In a large mixing bowl, whisk together the eggs and caster sugar until the mixture has tripled in volume. This will take about 3 to 5 minutes using a stand mixer or handheld electric mixer.
Add the melted butter, vanilla and milk to the eggs, and mix through on a low speed until just combined. Whisk together the flour, baking powder and salt. Add the flour to the wet ingredients and mix together at a low speed just until you have a smooth cake batter.
Pour the cake batter into the cake tin. Then pour the cinnamon sugar (reheat this mixture if necessary until you have a pouring consistency) over the top of the batter. Using a knife or the back of a spoon, swirl the cinnamon sugar mixture into the cake batter. Bake for 35-40 minutes or until a tester or toothpick just comes out clean from the centre of the cake.
Remove the cake from the oven and allow it to cool in the tin for at least 30 minutes before turning it out onto a wire rack and then onto a plate or cake stand.
In a bowl, whisk together the cream cheese, vanilla, lemon juice and icing sugar until you have a nice pourable but thick icing sugar. Drizzle over the top of a cold cake. Slice and serve.