Prep: Preheat oven to 350 degrees F. Top a rimmed baking sheet with a baking rack and lightly spray with cooking spray; set aside. Flatten Chicken: Place chicken breasts between two sheets of plastic wrap and pound to an even thickness of 1/4-inch using the flat side of a meat mallet or side of a can (they will spread out a lot). Layer: Lay 2 slices of ham over each chicken breast. Evenly line a heaping 1/4 cup shredded cheese down the center of the ham, leaving about 1/2-inch border on all sides.
Roll Chicken: Starting on the smaller end of the chicken, tightly roll up, folding the ham over the cheese on the end (to prevent it from oozing out). Secure with toothpicks.
Panko Breading: In a large skillet, melt 1 1/2 tablespoons unsalted butter in 1 1/2 tablespoons olive oil over medium heat. Add the panko and stir to coat. Continue cooking until the crumbs become golden brown, then immediately transfer to a large shallow dish (like a cake pan or pie plate). Once cool, stir in the Parmesan and breading spices. Dijon Wash: In a separate large shallow dish, whisk together 2 tablespoons Dijon mustard, 2 tablespoons honey, and 2 tablespoons olive oil. Working with one chicken roll at a time, add chicken to the Dijon Wash and brush to evenly coat. Bread Chicken: Transfer to the breading and press the crumbs into all sides, turning as needed. Transfer to the prepared baking rack, leaving a few inches between each roll.
Bake: Bake chicken at 350 degrees F until cooked to an internal temperature of 160 degrees on an instant read thermometer (this one is my favorite), about 30-35 minutes. Check the chicken the last 10 minutes of baking, and top with foil if necessary to prevent excess browning. Transfer chicken to a cutting board and allow to rest for 5 minutes before slicing. The last few minutes of baking, make the Dijon Cream Sauce (or make early and reheat): Dijon Cream Sauce: Whisk all of the ingredients together in a large saucepan. Bring to a boil then reduce to a simmer until thickened. The sauce will be on the thin side, but will thicken once removed from the heat.
Serve: Serve the Dijon Cream Sauce over the sliced chicken; garnish with parsley if desired.