What makes this cake classic? In our book, a "classic" yellow cake — read, '60s box-mix style, like Mom used to make — is marked by its pleasing moistness, its easy sliceability (no crumbling, please) and simple vanilla flavor. This cake has it all, and more: the fudge frosting on top is, well, the icing on the cake!
Preheat the oven to 350°F. Lightly grease a 9" round cake pan that's at least 2" deep; for extra protection against sticking, line the pan with parchment, and grease the parchment.
To make the cake: Beat together the sugar and butter until thoroughly combined.
Add the eggs one at a time, beating well and scraping the bowl after each. After you've added the second egg, beat at high speed for 2 minutes; the batter will lighten in color and become fluffy.
Add the vanilla, almond extract, salt, baking powder, and baking soda, stirring to combine.
Starting and ending with the flour, alternately add the flour and yogurt to the mixture: 1/3 of the flour, half the yogurt, 1/3 of the flour, the remaining yogurt, and the remaining flour. Beat gently to combine after each addition. Scrape the bottom and sides of the bowl, and beat briefly.
Spoon the batter into the pan. Bake the cake for 30 to 35 minutes, until it's golden brown on top, the edges are beginning to pull away from the sides of the pan, and a toothpick inserted into the center comes out clean, or with a few moist crumbs clinging to it.
After 10 minutes, turn the cake out of the pan onto a rack to cool completely before frosting.
To make the frosting: Sift the confectioners' sugar into a mixing bowl.
Melt the butter in a small saucepan. Stir in the cocoa and yogurt.
Bring the mixture to a boil, then remove from the heat. Stir in the vanilla and espresso powder. Add to the confectioners' sugar in the bowl, beating until smooth.
Quickly pour over the cooled cake, while the frosting is still warm.
