Preheat your oven to 350°F (175°C) and prepare two 9-inch round cake pans. Grease the pans with butter and lightly flour them to prevent sticking.

In a medium mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt, ensuring an even distribution of the leavening agents. Set this mixture aside.

In a large mixing bowl, use an electric mixer to cream the unsalted butter with both granulated sugar and light brown sugar until light and fluffy, about 3-5 minutes.

Add the eggs one at a time, mixing well after each addition. Follow with the vanilla extract, ensuring everything is well-combined and smooth.

Gradually mix the reserved dry ingredient blend into the butter mixture, alternating with the buttermilk. Begin and end with the dry mixture.

Carefully fold in the melted and slightly cooled white chocolate into the batter using a spatula.

Divide the batter evenly between the prepared cake pans and smooth the tops with a spatula. Bake for 25-30 minutes.

Allow the cakes to cool in the pans for about 10 minutes before transferring to a wire rack to cool completely.

For the frosting, beat softened cream cheese and butter together in a mixing bowl until smooth and creamy. Gradually incorporate confectioners' sugar, followed by the melted white chocolate and vanilla.

Once the cakes are cooled, place one layer on a serving plate, spread frosting on top, place the second layer on it, and continue to frost the top and sides.