Preheat oven to 160 °Celsius. Prepare four 5-inches round baking trays (greased and floured). If you don't have 4 tins, bake the cakes in batches.
Sieve flour, baking powder and salt and keep it aside.
In a clean bowl, cream the butter, and sugar until light and fluffy. Add the eggs and continue beating until it is well incorporated and the mixture is all light and creamy.
Fold in the flour alternately with milk, starting and end with flour.
Finally, add the vanilla extract and mix well.
Pour cake batter into prepared tins and bake for about 25 to 30 minutes until the center of the cakes spring back when pressed lightly. You can also use a toothpick to test if the cake is done. The toothpick should come out without any wet batter sticking to it when inserted in the center of the cake.
Remove cakes from oven and let them rest in the tins for a few minutes before turning them over onto wire racks to cool completely.
To assemble the cake, level each layer and sandwich them with buttercream. Cover the sides and top with buttercream.