Preheat the oven to 350 F. Line four 8x2-inch cake pans with parchment, and spray the parchment with nonstick cooking spray. (Two 8x3-inch pans can be used instead, you will just have to adjust the cooking time.)
In a large bowl, sift together the flour, baking powder, baking soda, and salt, and set aside for now.
Melt the white chocolate in a small bowl in the microwave, stirring after every 30 seconds to prevent overheating. Set aside until the white chocolate is at room temperature but still fluid.
Combine the butter and 1 1/2 cups of sugar in the bowl of a large stand mixer fitted with a paddle attachment. Cream them together for about 5 minutes, until light and fluffy.
Stir 2 tablespoons of the butter mixture into the melted white chocolate, then add the chocolate back to the butter in the mixer, and mix on low speed until blended. Add the egg yolks in two batches, mixing well between each addition, then add the vanilla extract
With the mixer on low, alternate adding the flour with the buttermilk, starting and ending with the dry ingredients. Stop the mixer when just a few streaks of flour remain, and scrape down the bottom and sides of the bowl with a spatula.
In a separate mixing bowl, whip the egg whites until they're foamy and just starting to hold soft peaks. Add the remaining 1/4 cup of granulated sugar slowly, spoonful by spoonful, and continue whipping the whites until they are glossy and white and have the texture of shaving cream.
Gently fold the whites into the cake batter in 3 additions. Divide the batter evenly between the prepared pans. Bake the cakes in the 350 F oven for 20-25 minutes, rotating halfway through the baking. Bake until the cakes are golden brown and a toothpick inserted into the center comes out clean.
Cool the cakes on a wire rack, and once at room temperature, run a knife around the edge and gently flip them out of the pans. For the easiest assembly, wrap the cakes individually in plastic wrap and place them in the freezer until they're slightly frozen, for about 30 minutes. The cakes can be made in advance and stored in the freezer until you're ready to use them.