First make a Béchamel sauce:
Melt the butter in a pan over a gentle heat. When the butter has melted, add the flour and mix together using a wooden spoon until it starts bubbling gently. Then gradually add the cold milk in small quantities.
Separate the eggs, keeping only the yolks.
Away from the heat, beat the egg yolks thoroughly. Grate the Comté cheese and add to the mixture. Season and add the nutmeg.
Spread the mixture out in a dish and leave to cool in the fridge.
Make cylindrical shapes out of the dough (or cut into rectangles) and coat firstly in the flour, then in the seasoned beaten egg and finally in the breadcrumbs. For a thicker coating, you can dip the dough in the egg again and coat with more breadcrumbs.
Heat the vegetable oil to a temperature of 180°C and fry the melts and the parsley sprigs. Drain on kitchen paper.
Serve the melts with the fried parsley and lemon quarters.