Preheat your oven to 350°F (175°C). Prepare a 4-inch round cake pan by lining it with parchment paper or greasing it thoroughly.

In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy. Add in the egg (or applesauce) and vanilla extract, mixing until combined.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually combine this dry mixture into the wet ingredients, alternating with the milk. Mix until the batter is smooth.

Pour the batter into the prepared cake pan and spread it evenly. Bake in the preheated oven for 22–25 minutes or until a toothpick inserted comes out clean.

Let the cake cool in the pan for about 10 minutes before transferring it to a cooling rack. Once cooled, level the top and slice it horizontally into layers.

In a bowl, beat the softened butter until creamy. Gradually add powdered sugar and a splash of vanilla extract, beating until fluffy. Reserve some frosting for decorating.

Spread a layer of frosting between each cake layer. After stacking, chill the cake before applying a final layer of frosting on the outside. Decorate as desired.