Prepare the Cake:

1. Preheat the Oven: Set to 350°F (175°C). Grease and line two 9-inch round cake pans with parchment paper.
2. Sift the Dry Ingredients: In a medium bowl, whisk together flour, sugar, baking soda, salt, and cocoa powder.
3. Mix the Wet Ingredients: In a large bowl, whisk oil, buttermilk, eggs, vinegar, vanilla, red food coloring, and purple food coloring until smooth.
4. Combine the Batter: Gradually mix the dry ingredients into the wet ingredients until just combined. Do not overmix.
5. Bake: Divide batter evenly between the prepared cake pans. Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.
6. Cool the Cakes: Let them cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.

Prepare the Frosting:

1. Melt the White Chocolate: In a heatproof bowl, melt the white chocolate over a double boiler or in the microwave in 15-second intervals, stirring until smooth. Let cool slightly.
2. Beat the Butter and Cream Cheese: In a large mixing bowl, beat cream cheese and butter until light and fluffy.
3. Add Sugar and Chocolate: Gradually mix in the confectioners’ sugar, then stir in the melted white chocolate. Beat until smooth and creamy.

Assemble the Cake:

1. Frost the Layers: Place one cake layer on a serving plate and spread an even layer of frosting on top.
2. Stack and Frost: Add the second cake layer and spread the remaining frosting over the top and sides.
3. Chill: Refrigerate for at least 30 minutes before slicing to set the frosting.