In a large bowl, whisk the eggs, heavy cream, salt, and pepper vigorously for about 1 to 2 minutes until well combined and lightly frothy.
Heat a non-stick skillet over medium-low heat. Melt the butter until bubbling slightly.
Pour the egg mixture into the skillet. Let it sit undisturbed for about 30 seconds until the edges start to gently set.
Using a rubber spatula, slowly push the eggs from the edges to the center of the pan, forming large, soft curds. Continue folding gently.
Just before the eggs are fully set and while they still look slightly wet, remove the pan from the heat.
Gently fold in the chopped smoked salmon, fresh chives, and dill. The residual heat will finish cooking the eggs without making the salmon rubbery.
Divide the scrambled eggs evenly over the warm toasted sourdough slices. Garnish with additional fresh herbs and serve immediately with lemon wedges on the side.