Preheat the oven to 350°F/180°c. Line the base of 2 x 9 inch round cake tins with parchment paper, and grease the sides. Set aside.
Add the all purpose flour, brown sugar, baking powder, ground cinnamon and salt to a large mixing bowl. Whisk until well combined. Set aside.
Add the milk, oil, eggs and vanilla extract to another large mixing bowl. Whisk until well combined.
Pour the wet ingredients into the bowl with the dry ingredients. Mix until just combined. Fold through the grated carrot and chopped walnuts.
Divide the cake batter between the 2 cake tins. Bake for 30 minutes, or until cooked through. Allow to cool in the tins for 15 minutes before transferring to a cooling rack to cool completely.
To make the frosting, add the softened cream cheese, softened butter, vanilla extract and salt to the bowl of a stand mixer. Beat on a high speed using wire whisk attachment for 2 minutes or until smooth.
Add the powdered sugar to the bowl, one cup at a time, beating on a low speed to combine. Once all of the powdered sugar has been added, increase the speed to high and beat for 2 minutes or until pale and fluffy.
Place 1 of the cakes on a cake plate, and top with half of the frosting. Place the second cake over the first, then spread the rest of the frosting over the top.