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1
To make the cake, preheat the oven to 350F.
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2
Butter and flour two 9-inch round cake pans and line the bottom of each pan with parchment paper.
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3
Whisk together the flour, cocoa powder, baking soda, and salt in a small bowl.
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4
Beat the butter, sugar, and oil in a stand mixer fitted with the paddle attachment until light and fluffy.
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5
Add the eggs, one at a time, scraping down the sides of the bowl, and beat until incorporated.
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6
Beat in the vanilla, vinegar, and food coloring.
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7
Add the flour mixture to the batter in 3 batches, alternating with the buttermilk and mixing well after each addition.
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8
Divide the batter evenly between the prepared pans and bake for 30 to 40 minutes or until a wooden skewer inserted into the center comes out with a few moist crumbs attached.
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9
Cool on a wire rack for 15 minutes before removing the cakes from the pans.
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10
Let cool completely on the rack before frosting.
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11
To make the frosting, combine the cream, milk, and vanilla bean and seeds in a small saucepan and bring to a simmer over medium-high heat.
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12
Remove the vanilla bean and discard.
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13
Add the flour and cook, whisking constantly, until thickened to a paste, about 2 minutes.
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14
Scrape into a bowl, cover, and refrigerate until very cold, at least 3 hours.
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15
Combine the butter and sugar in a stand mixer fitted with the whisk attachment and beat until the mixture is very fluffy and the sugar is totally dissolved, about 6 minutes.
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16
Add the cold paste, a few tablespoons at a time, to the butter mixture and whip until light and fluffy.
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17
Slice each cake layer in half horizontally.
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18
Place one cake layer on a cake round and spread about one-fi fth of the frosting evenly over the top.
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19
Repeat to make 3 layers and top with the remaining cake layer, top side up.
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20
Use the remaining frosting to frost the top and sides of the cake.
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21
The cake will keep for up to 8 hours at cool room temperature.
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22
To serve, slice the cake into pieces.
