Prepare the chicken: Place a half chicken breasts skin side up on a sheet of plastic wrap. Cover it with a second sheet of wrap and, with a flat (not textured) wooden mallet, lightly beat it until flattened to a uniform thinness of less than ¼ inch. Set aside. Repeat this operation for all four pieces.
Prepare the breaded ingredients: Cut the ham and cheese into thin slices, 2 inches wide and 3 inches long. Break the egg into a shallow bowl and beat until smooth, adding a pinch of salt and pepper. Spread the crumbs on a second shallow bowl. Spread the flour on a dinner plate.
Bread the cordon bleu: Lay the chicken pieces on a flat work surface, skin side down. Lightly brush the inside of each breast with a little mustard. Don't use too much or the mustard will overpower the other flavors. Stack 2 half slices of cheese and a slice of ham in the center of each breast. Fold over the small side of the breast, then fold each end up, like an envelope, and finally fold over the large side. Make sure that the filling is completely encased.
Roll the chicken first in the flour, shake off the excess, and then dip each breast in the egg, allowing the excess to flow back into the bowl. Lay it in the crumbs. Roll it carefully so that it doesn't open up, patting the crumbs into all sides. The breadcrumbs should not get inside the folds or they won't stay closed when it cooks. When the piece is coated, lay it on a clean, dry plate and repeat until all the pieces are breaded. Set aside for at least half an hour to allow the breading to set. You may prepare the chicken several hours or even a day ahead up to this point. Cover and refrigerate, but take the pieces out at least half an hour before cooking.
Cook the cordon bleu: Heat a heavy skillet with the oil and butter over medium-high heat. Add the chicken and fry until golden brown all around for about 4 to 5 minutes. Then, bake in a preheated oven for 10 minutes at 425°F.
Serve: Place the cordon bleu on a paper towel to absorb any extra fat, and serve at once. Garnish with lemon wedges.
Description A delicious French classic: chicken rolled around ham and Swiss cheese. The quality of the ingredients you will use for this recipe will either make it a great dish or an exceedingly dull one.