Preheat oven to 425 degrees.
Using a meat mallet, flatten the chicken breasts till they are ½" thick. Sprinkle lightly with salt and pepper on each side.
Place slice of ham on laid out chicken, then top with slice of Swiss cheese.
Tightly roll the chicken breast and then secure with a toothpick. Trim off any dangling pieces of chicken if desired.
Combine melted butter, thyme, breadcrumbs and Parmesan and mix to combine. Add salt until it tastes noticeably salty, but not overwhelmingly so. Beat eggs in separate dish.
Working in batches, lightly dust the exterior of the rolled chicken with flour, being careful not to flour the interior rolled portion.
Dip chicken into beaten eggs and let excess egg drip off.
Roll the chicken into the breadcrumb mixture till it is evenly coated and place on greased baking sheet.
Place in oven and bake for 30 minutes, or until interior reaches 165 degrees.
Remove from oven, let rest for 5 minutes and serve.