In a bowl, beat together the eggs and chives with some freshly ground black pepper.
Melt 40g of the butter in a small, non-stick pan over a medium-low heat. When hot, add the eggs and gently cook, stirring occasionally, for 3 minutes or until softly scrambled.
Meanwhile, toast the bagels and spread with the remaining butter. When the eggs are ready, remove them from the heat and fold through the smoked salmon trimmings. Divide the bagels among 4 plates and spoon over the salmon and eggs. Season with freshly ground black pepper and serve.