Melt the butter in a glass bowl over simmering water. Once the butter melts, whisk in the sugar and the egg yolks, and cook for 5 minutes, stirring constantly so that the eggs become ribbon-like and light in color (don't scramble.) Whisk in the coffee, cocoa powder, rum and almonds, and continue cooking, stirring constantly, until the mixture becomes smooth and creamy.
Transfer the cake mixture to a mixing bowl and set aside.
Preheat the oven to 375 degrees F.
Butter and flour a 9-inch round cake pan.
In a clean, separate mixing bowl, beat the egg whites until the just begin to stiffen and hold soft peaks. Be sure to stop before they form hard peaks. Gently fold the whites into the chocolate mixture. Pour the batter into the prepared pan and bake until firm and beginning to separate from the sides, about 30 minutes. Remove from the oven and allow to cool 30 minutes more. Flip cake over, dust with confectioners' sugar and cut into wedges before serving.