Preheat oven to 350 F and lightly grease a baking pan.
Place a chicken breast between two layers of plastic wrap. Using a meat mallet, pound the chicken to 1/4 inch thickness. Remove the top layer, then lay on one slice of ham and one slice of cheese. Tightly roll the breast into a log, and use the plastic wrap to secure it's shape. Repeat with remaining chicken.
Prepare three bowls for breading. One should have the flour with a dash of salt and pepper. One with the two eggs whipped. One with the panko, minced garlic, fresh thyme, melted butter, and a little more salt and pepper.
Remove the chicken from the plastic wrap. Then lightly coat in flour, dip in the egg, then coat in the bread crumbs. Transfer to a baking pan. Repeat for all roulades.
Bake until browned and cooked through, about 30-35 minutes.
Enjoy whole as a main dish or cut into pinwheels for appetizers.