Step 1: To make sauce melt butter in a medium saucepan over medium heat and then add flour and cook stirring for 1 minute and then slowly add milk, whisking until combined.
Step 2: Ans now whisk in mustard and continue whisking over a medium high heat until boiling and thickened.
Step 3: Remove from heat and stir in cheese and season with salt and pepper and then transfer to a heatproof bowl.
Step 4: Place tops and bottoms of muffins cut side up, on a large oven tray lined with baking paper and 1 tablespoon of the sauce over the base and the tops and spread evenly to the edges.
Step 5: Divide ham evenly over each muffin and spoon remaining sauce over ham and cook in a very hot oven (220C) for 5 to 6 minutes, or until golden brown and then remove from the oven.
Step 6: Meanwhile place 6 greased egg rings (7.5 cm in diameter) in a greased large, non-stick frying pan over a medium heat and break an egg into each ring and cook for 3 minutes before removing ring and then cook for a further 5 to 6 minutes or until cooked to your liking and remove from pan.
Step 7: To serve, stack 2 muffin halves together on each plate and top with eggs and garnish with chives.
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