Preheat your oven to 375°F (190°C) and grease a baking dish.
Pound the chicken breasts to an even thickness.
Place two slices of ham and two slices of Swiss cheese on each chicken breast, then roll tightly and secure with toothpicks.
In separate bowls, place flour, beaten eggs, and breadcrumbs mixed with salt, pepper, garlic powder, and paprika.
Dredge each rolled chicken breast in flour, dip in egg, then coat with breadcrumbs.
Heat butter in a skillet and lightly brown the chicken on all sides.
Transfer the chicken to the prepared baking dish and bake for 25-30 minutes until golden and cooked through.
While baking, prepare the sauce: In a saucepan, heat heavy cream over medium heat.
Whisk in Parmesan cheese, Dijon mustard, and thyme. Simmer for 3-5 minutes until thickened.
Remove chicken from the oven, drizzle with sauce, and serve warm.