Butter a 10-inch round cake pan and line the bottom with waxed or parchment paper. Flour the sides of the pan with matzo cake meal.
In the top of a double boiler set over barely simmering water, melt the butter and chocolate together, stirring frequently. Set aside to cool slightly.
In a mixer fitted with a whisk attachment (or using a hand mixer), whip the eggs, egg yolks, and sugar until very light and fluffy. Fold in the hot chocolate mixture.
In a small bowl, mix the matzo meal and ground walnuts. Fold into the chocolate-egg mixture. Pour into the prepared pan and bake until firm and dry on the top and a toothpick inserted into the center comes out almost clean (a few crumbs are OK), about 35 to 40 minutes.
Let cool 20 minutes in the pan, then turn out onto a rack and let cool to room temperature. Transfer to a serving plate and refrigerate 1 hour.
Meanwhile, make the frosting: In the top of a double boiler set over barely simmering water, whisk the egg whites and sugar together until the mixture is very hot and the sugar has dissolved somewhat. Remove from the heat and whip the mixture in a mixer (or using a hand mixer) until cooled, smooth, and fluffy. Add the butter and whip until smooth; the mixture might look broken at this point, but keep whipping and it will smooth out.
Drizzle in the melted chocolate and coffee, and whip until smooth and fluffy. Using a flexible spatula, frost the chilled cake on the top and sides.
Serve immediately or refrigerate up to 24 hours. Remove from the refrigerator 1 hour before serving.
Recipe courtesy of "Butter Sugar Flour Eggs" by Gale Gand, Rick Tramonto, Julia Moskin: Clarkson N. Potter Publishers, 1999