Crack the eggs into a bowl and whisk them lightly. Add the heavy cream, a pinch of salt, and black pepper. Mix until just combined.

Heat a non-stick skillet over medium-low heat. Add the butter and let it melt, ensuring it coats the pan evenly.

Pour the egg mixture into the skillet. Let it sit for a few seconds until the edges start to set.

Gently stir the eggs with a spatula, folding them over as they cook. Keep the heat low to avoid overcooking.

When the eggs are soft and slightly runny (they will continue cooking off the heat), remove the skillet from the stove.

Divide the scrambled eggs onto plates. Top with slices of smoked salmon, sprinkle with fresh chives and lemon zest if using. Serve immediately.