Have all ingredients at room temperature.
1. Preheat oven to 350 degrees F. Grease and flour two 9 inch round cake pans or two 8 inch round cake pans.
2. Over a sheet of waxed paper, sift together the flour, baking powder and salt; set aside.
3. In a small bowl, combine the milk and vanilla; set aside.
4. In the bowl of an electric mixer fitted with the flat beater, beat the butter on medium speed until smooth, about 2 minutes.
5. Add the granulated sugar and beat until light and fluffy, about 5 minutes.
6. Add the eggs one at a time, beating well after each addition.
7. Reduce the speed to low and add the flour mixture in three additions, alternating with the milk mixture and beginning and ending with the flour. Beat each addition until just incorporated, stopping the mixer occasionally to scrape down the sides of the bowl.
8. Spoon the batter into the prepared pans and spread the batter evenly. Bake until the cakes begin to pull away from the sides of the pan and a toothpick inserted into the center comes out clean, 25 to 30 minutes.
9. Transfer the pans to a wire rack and let the cakes cool in the pans for 15 minutes, then turn them out onto the rack and let cool completely.
1. In a heatproof bowl set over but not touching simmering water in a saucepan, melt the chocolate; let cool to room temperature.
2. In the bowl of an electric mixer fitted with the flat beater, beat the butter on medium speed until smooth, about 30 seconds.
3. Add the confectioners' sugar and beat until smooth, creamy and slightly fluffy, about 3 minutes.
4. Beat in the melted chocolate, scraping the sides and bottom of the bowl to evenly distribute the chocolate.
1. Place one cake layer, top side down, on a serving plate.
2. Using an icing spatula or a knife, spread some of the frosting evenly on top.
3. Place the other layer, top side down, on the first layer.
4. Spread the frosting over the top and sides of the cake.
5. Refrigerate the cake 30 minutes before serving to set the frosting.
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