Roll 2 cheese slices inside 2 ham slices, then roll it all up and place in the chicken (see picture below). Seal with toothpicks.
Place the flour in a large bowl, the breadcrumbs in another bowl (or tray). Whisk the egg and place in a large bowl. You should have 3 separate bowls (or tray) to assemble the cordon bleu.
Dip the chicken breast in flour, then egg, then breadcrumbs. Repeat the operation with the other chicken breast.
Transfer to a baking tray then drizzle with olive oil.
Bake for 25 minutes. Remove toothpicks before serving.
B. Make the béchamel sauce
In a small saucepan, melt butter over medium heat. Add the flour in one go and stir for about 1 minute.
Add half the milk and whisk until the mixture is smooth.
Add the remaining milk, the mustard and parmesan. Cook for a few minutes, whisking constantly, until the sauce is smooth and slightly thickened. Please note that it will continue to thicken as it cools.