Chop the smoked salmon into small pieces.
Mix the salmon with cream in a bowl and let sit for 30 minutes.
Preheat your grill to the highest setting.
Slice the brioche tops, hollow out some bread, and toast both halves.
Melt butter in a saucepan over low heat.
Beat eggs softly with salt and pepper, then pour into the pan with foaming butter.
Stir eggs continuously over slightly higher heat until 50 percent solidified.
Add the salmon and cream mixture and stir vigorously for 3 minutes until thickened.
Remove from heat and stir until eggs are soft and creamy.
Fill the brioche buns with eggs, garnish with dill, and replace lids.