Preheat oven to 180 C / Gas 4. Grease and flour three 23cm cake tins.
Cream 600g caster sugar, 350g butter and 5 eggs together in a bowl. Beat well.
Combine flour, baking powder and 1/4 teaspoon salt. Add to the creamed mixture alternately with milk. Add vanilla extract. Beat until cake mixture makes ribbons when falling from the whisk or beater. Divide cake mixture among the prepared cake tins.
Bake in the preheated oven until a skewer inserted in the centre comes out clean, about 30 minutes. Cool layers on a rack before icing, at least 1 hour.
Combine soft brown sugar, 225g butter and 1/4 teaspoon salt in a saucepan over medium heat. Stir until brown sugar is dissolved, about 3 minutes. Add evaporated milk and continue stirring. Bring to a gentle boil and let bubble for about 4 minutes, stirring constantly to avoid sticking. Remove from heat and allow to cool, about 5 minutes.
Mix icing sugar and vanilla extract into the mixture using an electric beater until icing caramelises and thickens to the desired consistency.
Spread icing onto the cooled cake layers. Stack layers; ice top and sides.