Prepare the oven and pan

• Preheat the oven to 175 °C.
• Grease and line a small cake pan.

Mix the dry ingredients

• Whisk together the flour, baking powder, baking soda, cinnamon, nutmeg and salt in a bowl.

Mix the wet ingredients

• Whisk the brown sugar, oil and egg until smooth and slightly pale.

Make the batter

• Fold the dry ingredients into the wet mixture until just combined.
• Stir in the grated carrot and chopped walnuts.

Bake the cake

• Pour the batter into the prepared pan and smooth the top.
• Bake until a skewer inserted in the centre comes out clean.
• Let the cake cool completely in the pan before frosting.

Brown the butter

• Melt the butter in a saucepan over medium heat.
• Cook, swirling, until the milk solids turn golden and smell nutty.
• Pour into a bowl and let cool until firm but spreadable.

Make the frosting

• Beat the softened cream cheese with the cooled brown butter.
• Add the powdered sugar and vanilla and beat until smooth and creamy.

Frost and serve

• Spread the frosting generously over the cooled cake.
• Slice and serve.