Have all ingredients at room temperature, about 70°F. Preheat the oven to 350°F. Grease and flour two 9-inch round cake pans and line the bottoms with rounds of parchment paper. For a high-altitude chocolate cake, see here.
Melt in a double boiler or heatproof bowl set over a pan of barely simmering water:
Sift together in a medium bowl:
Combine in a measuring cup:
Beat in a large bowl, or in a stand mixer with the paddle attachment, until creamy:
Add and beat until very fluffy, about 5 minutes:
Scrape down the sides of the bowl and add:
Add one at a time until fully combined:
Scrape down the sides of the bowl. On low speed, add the flour mixture to the butter-sugar mixture in 3 parts, alternating with the milk mixture in 2 parts, beating until smooth. Fold in the melted chocolate. Scrape the batter into the prepared pans, smoothing the top. Bake until a toothpick inserted into the center comes out clean, 25 to 30 minutes.
Let cool in the pans on a rack for 10 minutes. Invert the cakes onto the rack, peel off the parchment, and turn right side up to cool completely.
Fill and frost with: