Melt the chocolate on the defrost setting, or 50% power of your microwave. (Or over a bowl of simmering water)
Mix the flour, cocoa powder, and baking soda into a small bowl along with the ground walnuts.
Cream the butter using a hand mixer or in the bowl of a stand mixer.
Add both sugars and beat until fluffy.
Beat in eggs 1 at a time.
Beat in vanilla, then melted chocolate.
Add dry ingredients alternately with buttermilk in 2 additions each, beating just until blended after each addition.
Spread the batter into the pan and bake until a tester inserted into center comes out with a few moist crumbs attached, about 35 minutes. Cool cake in pan on a rack.
For the icing, melt the chocolate as above and set aside. In a large bowl cream the butter and add in the sugar and cocoa powder, beating until smooth. Beat in 2 tablespoons of buttermilk and the vanilla. Beat in the melted chocolate. Thin with buttermilk if it's too stiff to spread nicely. This makes enough frosting to cover the cake with a thick layer, but I like it just on top.
I think it would be fairly easy to make this cake gluten free, either with a good gluten free baking mix in place of the all purpose flour, or maybe even almond flour. If you eat gluten free you'll also love my Amazing Quinoa Chocolate Cake!