Ingredients

• 8 large eggs
• 3/4 tsp. kosher salt, plus more
• 6 Tbsp. unsalted butter, divided
• 4 (1"-thick) slices sourdough or country-style bread
• 3 Tbsp. crème fraîche or sour cream
• 1 skin-on, boneless smoked trout fillet (about 5 oz.), skin removed, flesh broken into 1" pieces
• 1 lemon, halved
• Freshly ground black pepper
• 2 scallions, thinly sliced on a diagonal
• 2 Tbsp. coarsely chopped dill
• 4 oz. mature arugula, tough stems trimmed (about 4 cups)
• 2 tsp. extra-virgin olive oil

Instructions

1. Crack eggs into a medium bowl and add 3/4 tsp. salt. Whisk until no streaks remain.
2. Heat 2 Tbsp. butter in a large nonstick skillet over medium. As soon as foaming subsides, add 2 slices of bread and cook until golden brown underneath, about 3 minutes. Transfer to plates, cooked side up. Repeat with another 2 Tbsp. butter and remaining 2 slices of bread. Season toast with salt. Wipe out skillet and let it cool 3 minutes.
3. Heat remaining 2 Tbsp. butter in reserved 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 1 minute.
4. Spoon eggs over toast and top with trout. Finely grate lemon zest from one of the lemon halves over trout, then squeeze juice over toast. Season with pepper; scatter scallions and dill on top.
5. Squeeze juice from remaining lemon half into a medium bowl. Add arugula and drizzle with oil; season with salt and pepper. Toss to coat. Mound alongside toasts.