Begin by preheating your oven to 350°F (175°C). Lightly grease a square cake pan pan with butter or oil. You can also line the bottom with parchment paper for easy release later.

In a large mixing bowl, cream together the softened butter and granulated sugar using an electric mixer on medium speed. Beat for about 2–3 minutes until the mixture becomes light and fluffy.

Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract. Scrape down the sides of the bowl to ensure everything is fully incorporated.

Add the sourdough starter discard and milk to the mixture. Mix until smooth and fully combined. The batter may look a bit loose or curdled at this stage—this is normal.

In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Slowly add this dry mixture into the wet ingredients, mixing just until no flour streaks remain. Be careful not to overmix, which can result in a dense cake.

Pour the batter into your prepared cake pan and smooth the top with a spatula. Bake in the preheated oven for 30–35 minutes or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.

While the cake cools, prepare the buttercream by beating the room-temperature butter until creamy. Gradually add in the powdered sugar, alternating with the heavy cream, until the frosting reaches your desired consistency.

Stir in the vanilla extract and salt. Once the cake is fully cooled, frost the top and sides generously. Slice and serve.