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1
make the cake Preheat the oven to 350; arrange 3 racks in the oven.
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2
Line three 12-by-17-inch baking sheets with parchment paper and spray with vegetable oil.
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3
make the cake In a large bowl, whisk the cake flour with the baking powder and salt.
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4
In a measuring cup, combine the milk and vanilla.
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5
In the bowl of a standing electric mixer fitted with the paddle, beat the butter until creamy.
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6
Add the sugar and beat at medium speed until fluffy, about 5 minutes.
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7
Add the eggs, one at a time, beating well between additions.
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8
At low speed, beat in the dry and wet ingredients in 3 alternating batches.
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9
make the cake Spread the batter (there will be about 14 cups) evenly on the 3 baking sheets.
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10
Bake for about 30 minutes, just until springy; shift the pans halfway through for even baking.
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11
Let the cakes cool completely in the pans.
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12
make the cake Dust the cake tops generously with confectioners sugar.
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13
Invert the cakes onto cutting boards or sturdy cardboard and remove the sheets and peel off the parchment.
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14
Shake the boards to make sure the cakes dont stick.
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15
make the frosting and filling In a very large saucepan, combine 3 1/2 cups of the cream with the sugar and bring to a boil.
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16
Simmer over low heat for 10 minutes, stirring until slightly reduced.
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17
Remove from the heat.
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18
Add the chocolate.
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19
Let stand for 5 minutes, then whisk until smooth.
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20
Let the ganache cool.
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21
make the frosting and filling Using an electric mixer at moderate speed, beat the remaining 1/2 cup of cream into the ganache.
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22
Add the butter and beat until creamy, about 1 minute.
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23
Transfer half of the ganache (about 3 1/2 cups) to a bowl and beat in the confectioners sugar to make the filling.
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24
make the frosting and filling Immediately spread half of the filling over the top of a cake layer.
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25
Top with a second layer and spread with the remaining filling.
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26
Top with the third cake layer.
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27
Chill for 20 minutes.
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28
make the frosting and filling Trim the cake neatly.
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29
Slide parchment paper strips under the cake to catch frosting.
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30
Spread a thin layer of frosting around the side of the cake, then top with the remaining frosting.
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31
Refrigerate until set, about 2 hours.
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32
make the frosting and filling Remove the paper strips.
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33
Bring the cake to room temperature before serving.