Whisk eggs with milk and a pinch of pepper in a bowl. Go easy on the salt since smoked salmon brings plenty of saltiness.
Melt butter in a nonstick pan over medium-low heat until it foams.
Pour in the egg mixture and cook slowly, stirring constantly with a silicone spatula in gentle circular motions until soft curds begin to form.
When eggs are almost set but still slightly wet, add the salmon strips and gently fold them in.
Remove from heat while eggs are still creamy - they'll continue cooking from residual heat.
Sprinkle with fresh chives and serve immediately.