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For the Cake:
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1. Preheat oven to 335u00b0F and place rack in middle position. Line the bottom of two 9-inch round pans with parchment paper.
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2. Combine milk and vanilla in a bowl. Combine flour, baking powder and salt in separate bowl. Set aside.
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3. Using a spatula, toss 2 tablespoons of the wet ingredients with the chocolate chips in a small bowl. Add 1/4 cup of the dry ingredients. Toss again to coat evenly. This will keep the chocolate chips from sinking to the bottom of the cake. Set aside.
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4. Mix butter and sugars in the bowl of a standing mixer fitted with paddle attachment until well creamed, about 3 minutes.
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5. Add egg and egg yolk one at a time.
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6. Alternately add dry and wet mixtures about a quarter at a time into the creamed mixture, without pausing between additions.
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7. Remove the bowl and fold in the chocolate chips with a spatula. The dough will be thick - more like cookie dough than cake batter.
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8. Divide dough into prepared pans. It will be too thick to fill the pan to the edges, but will spread under the heat of the oven. Bake for 30-35 minutes or until edges crown and surface is browned.
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9. Cool the cakes in pans to room temperature, then invert them onto a rack using a small offset spatula to release edges.
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10. Make ganache (directions follow). Spread a thick layer between the two cakes. Dust the top with confectioner's sugar. Shave dark chocolate and sprinkle on top.
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For the Icing:
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1. In a saucepan over medium heat, bring cream and sugar to a light simmer, stirring occasionally. Place the butter, chocolate, vanilla, and sea salt in a large heatproof bowl.
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2. Pour hot cream over ingredients in the bowl and let stand for a few minutes to melt the chocolate. Whisk until smooth and set aside to cool, but do not refrigerate. Be patient, it will set up.
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3. Once the icing has thickened, stir it with a flexible spatula to a spreadable consistency.