Poke holes all over the baked cake using the end of a wooden spoon or the thick end of a chopstick.
In a medium microwave safe bowl, add the sweetened condensed milk, butter, and brown sugar. Heat in the microwave on high for 1 minute. Stir well, then continue microwaving in 30-second intervals until the butter is melted and the sugar has dissolved. Stir until smooth.
Pour the hot filling over the whole cake. Set the cake aside for at least 15 minutes to allow the wet mixture to soak into the cake.
In a large mixing bowl, beat the softened butter and cream cheese together with an electric mixer on medium speed until well combined.
Add the vanilla and heavy cream and mix until blended.
Add the powdered sugar and beat with the electric mixer until the frosting is light and fluffy.
Scoop the frosting onto the cake and spread edge to edge. Dust with a little cinnamon if desired.
Slice the cake and serve at room temperature.