Preheat your oven to 350°F (175°C). Grease and flour two 8-inch round cake pans or line them with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, cream the softened butter and granulated sugar together on medium speed until light and fluffy, approximately 3-4 minutes. Add the eggs one at a time, ensuring each is fully incorporated before adding the next. Mix in the vanilla extract and the food colorings until the batter achieves a vibrant blue hue.

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

In a small bowl, whisk together the buttermilk and vinegar. Gradually add the dry ingredients and buttermilk mixture to the creamed butter mixture in alternating batches, beginning and ending with the dry ingredients. Mix on low speed until just combined. Avoid overmixing to ensure a tender cake.

Divide the batter evenly between the prepared pans and smooth the tops with a spatula. Bake in the preheated oven for 24-26 minutes, or until a toothpick inserted into the center of the cakes comes out clean. Remove from the oven and allow the cakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

In a large mixing bowl, beat the cream cheese and butter together on medium speed until smooth and creamy, about 3 minutes. Add the milk and vanilla extract, mixing until fully incorporated. Gradually add the powdered sugar, one cup at a time, beating well after each addition, until the frosting is light and spreadable.

Place one cake layer on a serving plate or cake stand. Spread an even layer of frosting over the top. Place the second layer on top and frost the top and sides of the cake. Smooth the frosting with a spatula or leave it slightly textured for a rustic look.