Cake: Preheat the oven to 200 degrees C and grease a round 20cm cake tin.
Separate the eggs and put the whites in the bowl of a stand mixer. Beat on high until foamy, then add 2 tablespoons of the sugar and beat to stiff peaks. Place in a separate bowl.
Add the butter and remaining sugar to the mixer bowl and beat until light. Meanwhile, melt the chocolate and water in the microwave, then whisk in the rum and egg yolks. Add chocolate mixture to the butter and beat well. Fold in the egg whites. Sprinkle the flour over that and gently fold in.
Place the batter in the cake tin and bake until it tests done, about 25 minutes. Cool about five minutes then invert on a serving plate. Spread a thin layer of apricot jam over the cake. Let cool.
Glaze: In a glass measuring jug, place the chocolate, sugar and water. Melt in the microwave, then whisk in the butter to make a smooth icing. Pour over the top and sides of the cake and smooth with a spatula. Chill until icing is set.