Lightly toast the brioche slices under a preheated grill until just golden, then turn over and lightly toast on the other side. Keep warm.
Break the eggs into a saucepan, add the measurement water and butter and beat together. Season generously with pepper.
Cook over a medium heat, stirring continuously, until just beginning to scramble. Add the Parmesan and continue to cook, stirring and watching carefully, taking care not to overcook the eggs, until the eggs are soft and slightly runny. Remove from the heat when almost cooked and stir in the crème fraîche and chives.
Pile on to the warm brioche slices and serve warm with a sauce of your choice, if liked.