Preheat the oven to 375°F Butter and flour the walls of two 9-inch round cake pans and then line each pan with a circle of parchment paper.
To make the cake, sift the flour, baking powder and salt together 3 times into a bowl or onto a piece of parchment and set aside.
In a mixer fitted with the whisk attachment, beat the butter on medium speed until its light and fluffy, 3 to 5 minutes. Add the granulated sugar and whip until it's blended. One at a time, add the eggs, mixing after each addition until well combined. Whip in the vanilla and almond extracts. With the mixer on low speed, add the flour mixture to the butter mixture in thirds, alternating with the milk and ending with the flour. Mix until just combined after each addition.
Pour the batter into the prepared cake pans and bake until the cakes are golden and firm to the touch, 25 to 30 minutes. Remove from the oven and let cool in the pans.
Meanwhile, make the frosting. In a mixer fitted with the whisk attachment, whip the butter on medium speed until it's light ans fluffy, 3 to 5 minutes. With the mixer on low speed, add the powdered sugar gradually. Mix in the melted chocolate, then the vanilla. Add the milk by spoonfuls until the frosting is spreadable but still thick and fudgy.
Remove the parchment from one of the cake layers and place the cake on a serving platter. Using an offset or small icing spatula, spread the top with some frosting. Place the second cake layer on the first, bottom-side up so the cake has a nice flat top. Remove the parchment and press down slightly to secure the layers. Frost the top and sides of cake.