Whisk eggs very well in a large bowl with a splash of water and season well with salt and pepper; set aside.

Melt butter in a large, nonstick skillet until foamy over low-medium heat, swirling it around to coat the pan bottom and up the sides a little bit. Add the eggs and cook gently for a minute or two, then begin to bring the edges in towards the center as they begin to set. Dot the surface with half of the smoked salmon and half of the cream cheese and continue to scramble the eggs until they are light and fluffy, but still a tad moist and not dry. Quickly dot the surface with remaining smoked salmon and cream cheese, add some snipped chives and fresh dill, to taste, and serve immediately.