A new twist on an old classic.
Melt the butter in a saucepan over a medium heat. Add the flour and stir until well combined. Fry for 2 minutes. Gradually add the milk, whisking continuously until the sauce has thickened. Stir in the mustard, nutmeg, and parmesan, and remove from the heat.
Cut bagels in half and lightly toast.
Smear a generous spoonful of white sauce on the cut side of each bagel base. Top with ham, another large spoonful of white sauce and finish with a slice of gruyere cheese. Place under the grill and cook until golden brown.
Meanwhile, heat the olive oil in a large non-stick frying pan. Fry eggs until cooked to your liking.
Place egg on top of grilled bagel and season with salt and pepper.