In a mixing bowl, crack the eggs and whisk them together with the milk or cream until well combined. Season the mixture with salt and pepper to taste.

Heat a non-stick skillet or frying pan over medium heat and add the butter or oil, allowing it to melt and coat the pan evenly.

Pour the egg mixture into the pan and let it sit for a few seconds until the edges start to set.

Using a spatula or wooden spoon, gently scramble the eggs by pushing them towards the center of the pan while tilting the pan to allow the uncooked eggs to flow to the edges.

Once the eggs are mostly cooked but still slightly runny, add in the chopped smoked salmon. Continue to stir and fold the eggs and salmon together until the eggs are fully cooked and the salmon is heated through.

Remove the pan from the heat and transfer the scrambled eggs with smoked salmon to a serving plate.

Serve immediately.