Preheat the oven to 335°F. Grease and line three 6-inch cake pans or two 8-inch cake pans.
Warm the milk gently, then add the chopped white chocolate. Let it sit for 5 minutes.
Stir until the white chocolate melts into the milk. If needed, warm in short 10-second intervals, stirring between each one.
Stir in the vanilla extract, then let the white chocolate milk mixture cool until just above room temperature.
In a separate bowl, whisk together the flour, baking powder, and salt.
In a large mixing bowl, beat the softened butter and sugar together until light and fluffy, about 1–2 minutes.
Add the egg whites one at a time, mixing well after each addition.
Add one-third of the dry ingredients and mix on low until just combined.
Add half of the white chocolate milk mixture and mix again.
Continue alternating the dry ingredients and liquid mixture until everything is combined. Do not overmix.
Divide the batter evenly between the prepared cake pans.
Bake for 25–35 minutes, or until a toothpick inserted into the center comes out clean.
Let the cakes cool in the pans for 10 minutes, then turn them out onto a cooling rack.
Chill the cake layers before filling and frosting for easier assembly.