To make a béchamel sauce, whisk together flour, cream and milk on low heat until all lumps are gone. Continue whisking over low heat until sauce thickens – approx. 10 minutes. Once the sauce is thick, remove from heat, add butter, chives and salt and pepper.
Toast 4 pieces of bread, then top each piece with approx. 3 tbsp. of the béchamel sauce and 2 slices of cheese. Place under broiler for 5-10 minutes until crispy.
Toast the other 4 slices of bread, top with more béchamel and 2 slices of ham.
Poach 4 eggs to your liking, then combine sandwiches and place your egg on top.