Steps:

• Preheat oven to 350 degrees F (175 degrees C). Grease and flour 2 9-inch cake pans. In a bowl, sift together the cake flour, chocolate pudding mix, cocoa powder, and salt.
• In a large bowl, beat 1/2 cup of butter with 1 1/2 cup of sugar with an electric mixer until creamy; beat the eggs in, one at a time, and beat until the mixture is fluffy, about 1 minute. Beat in the flour mixture, alternating with buttermilk, in several additions. Mix in 1 teaspoon of vanilla extract and the red food color until the batter is uniformly colored. In a bowl, stir the baking soda with vinegar, and gently fold the foamy mixture gently into the batter. Pour the batter into the prepared cake pans.
• Bake in the preheated oven until a toothpick inserted into the center of a cake comes out clean or with moist crumbs, about 30 minutes. Allow to cool completely before frosting.
• For frosting, place all-purpose flour in a saucepan, and gradually whisk milk into the flour, about 2 tablespoons at a time, until smoothly combined. Bring the mixture to a simmer over medium-low heat, whisking constantly until thickened and smooth; allow to cool completely. Beat 1 cup of sugar and 1 cup of butter in a bowl with an electric mixer until fluffy, about 1 minute, and gradually beat in the cooled milk mixture; add 1 teaspoon of vanilla extract. Beat the frosting until fluffy and spreadable, 1 to 2 more minutes.

Steps:

• Combine the cream cheese and butter on medium speed, just until blended, in the bowl of a stand mixer fitted with the paddle attachment. Stop and scrape down the sides of the bowl. Add the vanilla and salt and beat until combined. With the speed on low, add the powdered sugar in 4 batches, beating until smooth between each addition. Refrigerate for 5 to 10 minutes before using.