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For the Cake: Position rack in center of oven. Preheat oven to 350°F/180° Coat the insides of two 8-inch by 2-inch (20 cm x 5 cm) round cake pans with nonstick spray, line bottoms with parchment rounds, then spray parchment.
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Combine milk and vinegar and let sit for at least 5 minutes to thicken.
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Meanwhile, whisk together flour, cocoa, baking soda and salt in a medium bowl to combine and aerate; set aside.
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In a large bowl with an electric mixer on medium-high speed, beat butter until creamy, about 2 minutes. Add the sugar gradually and beat until very light and fluffy, about 3 minutes, scraping down the bowl once or twice. Beat in vanilla and red food coloring.
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Beat in the eggs one at a time, scraping down after each addition, allowing each egg to be absorbed before continuing. Add the flour mixture in four additions, alternately with the soured, thickened milk. Begin and end with the flour mixture and beat briefly until smooth. Divide batter evenly in pans.
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Bake for about 30 to 35 minutes or until a toothpick shows a few moist crumbs clinging. The cake will have begun to come away from the sides of the pan. Cool pans on racks for 5 minutes. Unmold, peel off parchment, and place directly on racks to cool completely. Layers are ready to fill and frost. Alternatively, place layers on cardboard rounds and double wrap in plastic wrap; store at room temperature if assembling within 24 hours.
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For the Icing: Whisk together milk and flour in a small saucepan. Bring to a simmer over medium heat, whisking constantly. Once it simmers, continue whisking and cook 1 to 2 minutes or until thickened, smooth and glossy. It should be thick enough for you to be able to see whisk marks. Remove from heat and set aside.
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Stir occasionally until cool. In a medium bowl with an electric mixer on medium-high speed, beat butter until creamy, about 2 minutes. Add sugar and beat on high speed until light and fluffy, scraping down the bowl once or twice.
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Beat in vanilla, then add cooled, cooked flour mixture and beat until smooth. Frosting is ready to use. If the frosting is not silky smooth, it is because it is too cool. Either keep beating or remove about 1 cup (240 ml), zap in microwave for 10 seconds to soften, then add it back to the main batch and beat vigorously. Repeat as needed. Trust me. This can make the difference between the frosting being just okay and truly ultra silky.
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Fill and frost the cake layers with prepared frosting and decorate as desired. This frosting is stiff enough to pipe, even though I chose to just use an icing spatula in the image. Cake may be served immediately or stored at room temperature for up to 3 days in a covered container.