Preheat the oven to 375 degrees F. Butter and flour 2 (9-inch) round cake pans and line the bottoms with parchment paper.
Sift the flour, baking powder, and salt together 3 times and set aside.
In a mixer fitted with a whisk attachment, cream the butter until smooth and fluffy. Add the sugar and mix until blended. Add the eggs, 1 at a time, mixing after each addition until blended. Add the vanilla and almond extracts and mix.
With the mixer running at low speed, and working in alternating batches, add the dry ingredients and the milk to the butter mixture, mixing just to combine after each addition. Mix until just smooth. Pour into 2 cake pans. Bake until risen, golden, and firm to the touch, about 25 to 30 minutes. Let cool in the pans.
For the frosting: In a mixer with a whip attachment, cream the butter well. Add the confectioners' sugar gradually. Add the melted chocolate, then the vanilla. Add the milk by spoonfuls until you have reached a fudgy yet spreadable consistency.
Once the cakes have cooled, place 1 layer on a serving platter and cover the top with frosting. Place the second layer on top of that but bottom-side up, to create a nice flat top. Press down to secure the layer. Frost the top and sides using a swirling motion. Or if you want it to look more professional, do a crumb layer of frosting, chill, then do a topcoat.