Break the eggs into a small mixing bowl, add the milk and a pinch of salt and pepper. Whisk until the eggs are frothy, about 30 seconds.
Melt the butter in a small (8-inch) nonstick fry pan over medium-low heat and add the eggs. Allow to set for about 30 seconds, then scatter the diced salmon and dill evenly over the top.
Working from the outer edges of the pan, gently draw a silicone (or rubber) spatula through the eggs toward the center to form soft, shiny curds.
Continue cooking in this manner until the eggs are no longer runny, but still look creamy and somewhat shiny. Remove from the heat and let stand 1 minute before serving.