Preheat your oven to 350°F (176°C). Prepare two 8-inch round cake pans by greasing them with cake release or lining them with parchment paper.

In a large mixing bowl, sift together the all-purpose flour, granulated sugar, baking soda, salt, and cocoa powder. Set aside.

In another bowl, whisk together the vegetable oil, milk, large egg, red food coloring, vinegar, and vanilla extract until fully blended.

Gently pour the wet mixture into the bowl with the dry ingredients. Stir just until combined.

Divide the prepared batter evenly between the two cake pans. Place them in the preheated oven and bake for 25-30 minutes.

Once baked, remove the cake layers from the oven and let them cool in the pans for about 10 minutes. Transfer to a wire rack to cool completely.

In a mixing bowl, beat the cream cheese and sweetened condensed milk together until smooth. Whip the heavy cream until stiff peaks form, then fold into the cream cheese mixture.

Transfer the ice cream mixture to a lined baking pan, smooth the top with a spatula, cover with plastic wrap, and freeze for at least 8 hours.

Melt the white chocolate in a microwave-safe bowl, let it cool slightly, then mix with cream cheese, unsalted butter, and sour cream until combined, gradually adding icing sugar.

Remove the first cake layer and place it on a serving platter. Spoon half of the ice cream filling over the cake, spread evenly, and top with the second layer. Frost the whole cake.

Return the assembled cake to the freezer for at least one additional hour before slicing and serving.