Preheat oven to 350°F. Use 2 muffin pans, each with 12 (1/2-cup) muffin cups, and line each cup with paper liner.

In a large bowl, on the medium speed of an electric mixer, cream the butter and sugar until very light and fluffy, about 5 minutes. Add the eggs, one at a time, beating well after each addition. In a small bowl, whisk together the food coloring, cocoa, and vanilla. Add to the batter and beat well.

In a measuring cup, stir the salt into the buttermilk. Add to the batter in three parts alternating with the flour. With each addition, beat until the ingredients are incorporated, but do not overbeat. In a small bowl, stir together the cider vinegar and baking soda. Add to the batter and mix well. Using a rubber spatula, scrape down the batter in the bowl, making sure the ingredients are well blended and the batter is smooth.

Divide the batter among the prepared cupcake tins. Arrange the oven racks in the upper and lower thirds of the oven and bake the cupcakes, switching positions of the pans halfway through baking, until a tester comes out clean, about 20 minutes. Cool the cupcakes in the pan for 10 minutes, then remove from the pan and cool completely on the rack before icing.

In a medium-size saucepan, whisk the flour into the milk until smooth. Place over medium heat and, stirring constantly, cook until the mixture becomes very thick and begins to bubble, 10-15 minutes. Cover with waxed paper placed directly on the surface and cool to room temperature, about 30 minutes.

In a large bowl, on the medium high speed of an electric mixer, beat the butter for 3 minutes, until smooth and creamy. Gradually add the sugar, beating continuously for 3 minutes until fluffy. Add the vanilla and beat well.

Add the cooled milk mixture, and continue to beat on the medium high speed for 5 minutes, until very smooth and noticeably whiter in color. Cover and refrigerate for 15 minutes (no less and no longer—set a timer!). Use immediately.