Not Deli Ham, but Prosciutto.  And not Swiss, Gruyere.  All good!

Ingredients

4 chicken breasts skinless and boneless

8 thin slices prosciutto di Parma  Note: Small chicken breasts need just one slice of prosciutto each, so 4 not 8.

6 oz. Gruyere, coarsely grated

1/4 cup all-purpose flour

Kosher salt and freshly ground black pepper

1 cup panko bread crumbs – may try Italian seasoned Panko next time

1/2 teaspoon dried thyme

1 clove garlic, peeled and pressed

2 tablespoons unsalted butter, melted

2 eggs

Extra-virgin olive oil

1. Preheat oven to 350 degrees F.
2. Lay a chicken breast between 2 pieces of plastic wrap. Using the flat side of a meat mallet, gently pound the chicken to 1/4-inch thickness. Remove the top sheet of plastic and lay 2 slices of prosciutto neatly over the top to cover the breast and sprinkle a quarter of the cheese over the prosciutto. Tuck in the sides of the breast and roll up tight like a jellyroll inside the plastic wrap. Squeeze the log gently to seal and twist both ends tight to form a nice log (roulade). Repeat with remaining chicken.
3. Season the flour with salt and pepper and put in a shallow bowl.
4. Mix the bread crumbs with thyme, garlic and kosher salt, pepper, and melted butter, and put in a shallow bowl.
5. Beat  the eggs and season (so the flour, the eggs and the crumbs are all seasoned), and put in a shallow bowl.
6. Remove the plastic wrap from the chicken. Lightly dust the chicken with flour, dip in the egg mixture, then gently coat in the bread crumbs.
7. Lightly coat a glass baking dish with olive oil and carefully transfer the roulades onto it. Bake for 25 minutes until browned and cooked through.  Note: Small breasts will cook in 25 minutes; large breasts will take up to 40.  Use a thermometer and or do a test slice or two.
8. Cut into pinwheels and serve.