To make the Bechamel sauce, melt butter in a saucepan, whisk in flour, and cook for 1 minute. Slowly whisk in the milk, stirring until thickened. Add Gruyère, season with salt and pepper, and stir until smooth.
Toast up the bread, fry an egg with butter, set aside.
Assemble the Sandwich by layering Bechamel sauce on the toast, with ham and pickles on top.
Place the fried egg on top of the sandwic, finish with more cheese and chives, and serve immediately.
