Preheat oven to 350°F.
Add flour, baking powder, baking soda, and salt to the bowl. Set aside.
In another bowl, mix together milk, and white vinegar.
In a large mixing bowl, cream softened butter with sugar using an electric mixer or a food processor. The butter mixture should be pale yellow, light, and fluffy. Then, scrape the sides of the bowl with a spatula. Add eggs (one at a time), mix until well combined. Then, stir in vanilla extract.
Gradually add the milk mixture and dry ingredients to the batter, mix each time until combined.
Grease a 10-inch bundt pan with flour and cooking spray (or butter). Transfer the batter to the pan. Bake in the preheated oven for 50-60 minutes. The butter cake is ready when a toothpick inserted in the center comes out clean.
Remove the cake from the oven. Let cool slightly while preparing the soaking syrup.
To make the soaking syrup: Combine sugar, butter, and brandy in a small saucepan over medium-low heat. Stir constantly until the butter melts (don't allow the syrup to boil). Turn off the heat. Add vanilla extract. Mix until combined.
Poke holes all over the cake with a skewer. Evenly pour the syrup over the butter cake. Allow the cake to cool to room temperature in the pan (at least 30 minutes), then turn out onto a serving plate. I like to preserve some syrup and brush the butter cake before serving.