Preheat the oven to 400°F. Grease a 9X9 inch (or similarly sized) baking pan.
Place a Pyrex or other heat resistant bowl on top of a pot of just simmering (not boiling) water. The bottom of the bowl should be just above the water line. Crack the eggs into the bowl and whisk in the sugar. Whisk continually for ten minutes assuring that the water stays just at a simmer. The eggs will turn light colored and will thicken considerably. An electric whisk helps enormously.
After ten minutes, remove the bowl from the heat and stir in the finely chopped chocolate with a wooden spoon. Continue stirring until all the chocolate has melted and is incorporated in the batter.
Stir in the crème fraiche and mix until combined.
Stir in the flour and mix until combined.
Finish by gradually stirring in the rum.
Pour the batter into the baking pan and place in 400°F oven to bake for 30 minutes.
Remove from the oven and allow to cool for five minutes. Turn the cake onto a wire rack to finish cooling.