8 slicescrusty white bread, cut 1cm thick95 gm(1/3 cup) Dijon mustard, plus extra to serve4thick slices leg ham300 gmGruyère, coarsely grated100 gmbutter, coarsely chopped4eggsBéchamel60 gmbutter, coarsely chopped60 gmplain flour, sieved250 ml(1 cup) milk30 gmfinely grated parmesanPinchfinely grated nutmeg
For béchamel, melt butter in a saucepan over medium heat, stir in flour, cook until light golden (1-2 minutes), remove from heat. Meanwhile, heat milk in a separate saucepan over medium-high heat until simmering, then, whisking continuously, gradually add milk to butter mixture. Return to heat, stir until mixture just returns to the boil (3-4 minutes), stir in parmesan and nutmeg, season to taste, cover closely with plastic wrap and set aside until thick and cooled to room temperature.
Place four slices of bread on a work surface, spread with mustard, top with ham and Gruyère, sandwich with remaining bread.
Preheat grill to high. Melt half the butter in a large frying pan over medium heat until foaming, add sandwiches to pan and cook, turning once, until golden (2-3 minutes each side). Remove from pan, spread tops thickly with béchamel and transfer to a baking tray, then grill until golden (3-4 minutes).
Meanwhile, heat remaining butter in a large frying pan and fry eggs to your liking (3-4 minutes for soft yolks). Place an egg on each sandwich and serve hot with extra mustard on the side.