In a blender, combine eggs, all-purpose flour, milk, kosher salt, then blend until very smooth.
Carefully remove the cast-iron skillet from the oven, then add unsalted butter. Once melted, pour the batter into the pan then sprinkle with grated Parmesan cheese and thinly sliced chives. Transfer to the oven and cook.
While the Dutch baby bakes, combine crème fraîche, chopped dill, and lemon zest in a small bowl. Stir well.
Carefully remove the Dutch baby from the oven, then top with thin slices of smoked salmon and as much of the lemon dill crème fraîche as you like. Garnish with additional sliced chives or dill, then finish with freshly ground black pepper and a generous pinch of flaky sea salt. Enjoy!