Place the bagel halves in a toaster and toast until golden brown.
Whisk the eggs with a little salt, black pepper and the butter, then pour the mixture into a small non-stick saucepan. Place the saucepan over a low heat and allow the eggs to cook gently until they start to set. Using a wooden spoon, slowly pull the eggs towards the centre.
Keep the mixture moving until you have really creamy scrambled eggs. Make sure not to overcook the eggs - take them off the heat while they are still slightly runny and creamy. It’s a balance to judge, but when you taste them you’ll know what I mean.
Spoon the scrambled eggs over the toasted bagel halves and serve with chilli jam.