Preheat oven to 350F (175C). Grease an 8x8 inch square pan.

Combine brown sugar, sifted flour, baking powder, baking soda, and salt in a large bowl.

Cut in butter using a pastry blender or your fingers until the mixture resembles fine breadcrumbs.

Press half of the mixture evenly into the prepared pan.

Dissolve baking soda in milk in a separate bowl.

Add beaten egg and nutmeg to the milk mixture and whisk to combine.

Pour the wet ingredients over the remaining sugar and flour mixture.

Mix well until just combined.

Spoon the batter evenly over the pressed-in mixture in the pan.

Sprinkle chopped walnuts evenly over the top of the cake.

Bake in the preheated oven for 1 hour, or until a wooden skewer inserted into the center comes out clean.

Let the cake stand in the pan for 15 minutes before turning it out onto a wire rack to cool completely.