Step 1

Melt the butter in a bowl and mix with the olive oil. Set aside. In another bowl, mix the regular and panko breadcrumbs with the Parmesan cheese, herbes de Provence, and 2 teaspoons of the garlic powder. Set aside.

Step 2

Pat the breasts dry. Place each chicken piece on a cutting board. Lay plastic wrap over each chicken piece and pound with a mallet to about a ¼- to ½-inch thickness. (Be sure not to pound too hard because it may tear up the meat or create holes.) Repeat with all of the chicken pieces.

Step 3

Season each chicken piece with salt and pepper and the remaining garlic powder. (Be careful not to oversalt the chicken as it is quite thin and the cheese and ham are also salty.)

Step 4

Place 2 slices of ham and 1 slice of cheese in each piece of chicken and roll, making sure you tuck in the sides in as much as possible to prevent the cheese from oozing out too much while baking. Secure the roll with toothpicks.

Step 5

Dip each chicken roll into the melted butter-olive oil mixture, then roll it in the breadcrumb-Parmesan mixture. Make sure all the sides are well coated. Place in a casserole dish or on an ovenproof plate. Place in the refrigerator for at least 1 hour to ensure that the breadcrumbs adhere to the chicken.

Step 6

Preheat the oven to 375 degrees.

Step 7

When ready to bake, place each chicken roll on a rack set in a drip pan, making sure you don't overcrowd them. Bake in the oven until no longer pink in the middle, about 35-40 minutes. (The time depends on how thinly you pounded the chicken.) Remove from the oven and let cool slightly. Reserve ½ cup drippings for the sauce.

Step 8

In a small saucepan, melt the butter over medium heat. Whisk the milk and cornstarch together in a bowl and slowly pour into the saucepan. Add the drippings and whisk until the mixture is smooth and thickened.

Step 9

Add the Parmesan cheese, garlic powder, and herbes de Provence. Season with salt and pepper, to taste. Mix thoroughly until the cheese is melted. Transfer to a bowl and serve with the chicken.