Add the coffee, 2/3 cup (150 g) of the sugar and the egg yolks one by one to the hot mixture. Separately, beat the egg whites into hard snow with the remaining sugar and vanilla and then add them slowly to the other mixture.
Pour the resulting blend into pudding cups that have been greased ahead of time, 3/4 full. Put them in a water bath in the oven to bake. Serve the pudding with the frosting.
For the frosting: Mix the sugar, flour and egg yolks, half the cold milk with the vanilla. Stir well. Put the remaining milk and coffee to boil, then while stirring nonstop, add them to the first mixture.
Put to boil again and remove from the heat. Before serving, add the egg whites that you've beaten to hard snow.