Crack eggs into a medium bowl and add salt. Whisk well.
Squeeze juice from half into a medium bowl. Add arugula and drizzle with olive oil; season with salt and pepper. Toss to coat. Serve on the side.
Heat 2 Tbsp. butter in skillet over medium-low. Once butter is foaming, cook egg mixture, stirring with a heatproof rubber spatula in broad sweeping motions, until some curds begin to form but eggs are still runny, about 2 minutes. Stir in crème fraîche and cook, stirring occasionally, until eggs are barely set, about 2 minutes.
While eggs are cooking, toast bread, and butter the way you like it.
Spoon eggs over toast and top with fish, then squeeze juice over the fish. Season with pepper; scatter scallions on top.
You can add the fish cold, from the fridge, but I like to warm it up in a pan before adding. You can also use fresh trout. All good.
