Whisk the eggs. Then, into a medium bowl, pass the eggs through a fine-mesh strainer. Add the half-and-half and whisk until smooth. Add the pepper and whisk until well combined.
Heat a nonstick skillet on low heat and melt the butter. Pour the eggs into the skillet. Using a heat-resistant rubber spatula, stir the egg mixture over low heat to create soft, creamy curds. Continue to cook until soft and creamy, then sprinkle in the salmon. Cook until light and fluffy. Serve, garnished with chives. Serve with a toasted bagel.