Break the eggs into a medium bowl and beat with a whisk until fully combined.
Melt the butter in a heavy skillet over
medium-high heat. Once it starts to bubble rapidly and turn brown, add
the smoked trout. Cook for 1 minute, just to warm through.
Add the eggs to the pan and stir gently
with a wooden spoon or rubber spatula to prevent the eggs from burning
(see Note). When the eggs are almost set but still runny (this will take
a couple of minutes at most), remove the skillet from the heat and add
the parmesan and crème fraîche, stirring briefly to incorporate. Top
with the chives, and serve immediately.
NOTE: You need to work quickly so your
eggs don’t stick and you can incorporate the other ingredients, so make
sure you have all your ingredients prepped and beside you at the stove
when you begin cooking. The residual heat from the skillet will finish
cooking the eggs, so don’t worry that we ask you to pull them off the
heat when they’re still runny.