Season the chicken breasts with salt and pepper, as well as the grated garlic clove, and tenderize them between sheets of food wrap until they are roughly ¼-inch thick. Cover each chicken breast with 4 slices of cheese. For each one, place 3 slices of ham on top of the cheese, and then another 2 slices of cheese on top of the ham.
Roll up the topped chicken breasts tightly and wrap them in plastic food wrap. Tightly twist both ends closed. Chill the roulades for an hour.
Unroll the puff pastry, cut it in half and brush each half with mustard. Place a roulade in the middle of each piece of pastry, and wrap the pastry around the meat to create four beautiful rolls.
Beat the eggs together, paint the rolls with the mixture, and then use a fork to scratch a crosshatched pattern in the pastry. Cook the rolls for 30 minutes in a convection oven at 350°F.