This has to be one of the most sublime combinations: soft, creamy scrambled eggs, together with the subtle, smoky flavour of the salmon.
The salmon needs to be chopped fairly small for this, so if you're using offcuts you might still need to chop some of the larger pieces. I say chop here, but very often I use scissors. Either way, place all the salmon pieces in a small bowl, pour in the cream, give it all a good stir, cover the bowl and leave it aside for 30 minutes.
When you are ready to make the scrambled eggs, preheat the grill to its highest setting. Slice the top off each brioche, then carefully scoop out and discard half the bread from inside, then place each one, alongside its lid, under the grill, and lightly toast on both sides.
Now melt the butter in a medium-sized saucepan over a very gentle heat. While it's melting, break the eggs into a bowl and beat them lightly with a fork, seasoning with a little salt and freshly milled black pepper. When the butter has melted and begins to foam, swirl it around the edges of the pan, then pour in the beaten eggs. Increase the heat slightly and, using a wooden fork or a wooden spoon with a point, stir continuously backwards and forwards, getting right into the corners of the pan.
As soon as the eggs begin to solidify - after about one minute - and when you have about 50 per cent solid and the rest still liquid, quickly add the salmon and cream, then keep on stirring like mad until almost all the liquid has gone, which will take 3-4 minutes. Then remove the pan from the heat and continue stirring until the eggs become a soft, creamy mass. Taste to check the seasoning and spoon into the toasted brioche buns. Top with a little dill, replace the lids and serve immediately.