Cut the chicken breasts in half lengthwise. Using a flat head mallet, pound each slice between sheets of plastic wrap to ¼ inch (6 mm) thickness, working from the center to the edges.
Remove the top sheet of plastic and season each slice with salt and freshly ground ground pepper. Spread a teaspoon of dijon mustard on each. Add a slice or two of ham (depending on their size) and finish with cheese slices.
Roll the chicken as tight as you can using the plastic sheet from the bottom. Refrigerate the rolled chicken for about 30 minutes.
Meanwhile prepare three large plates, one with flour, one with beaten egg and one with breadcrumb and garlic mixture.
Working one at a time, dredge cutlets in flour, then dip in egg and coat with breadcrumbs.
Heat oil into a frying pan over medium heat.
Place about one or two chicken rolls at a time and fry for about 5 minutes on each side until golden brown and cooked through.
Transfer to a plate lined with paper towel to remove excess oil.
Serve alongside a fresh salad or your favorite side dish.