Preheat the oven to 350°F. Lightly coat a baking dish with cooking spray.
Mix both kinds of breadcrumbs, cheese, ¼ teaspoon salt, and ¼ teaspoon black pepper in a shallow bowl or dish. Add the olive oil and stir to moisten all of the breadcrumbs.
Slice each chicken breast crosswise so you have four thin pieces. Cover the pieces with plastic wrap and pound them to a thickness of ¼”. Uncover them and season them on both sides with the rest of the salt and pepper.
Place the ham on each chicken piece. If the ham is larger than the chicken, tear it in half and place the pieces so they don’t hang too far off the edges.
Top the ham with the shredded cheese. Roll each chicken piece up into itself like a jelly roll.
Place each roll in the breadcrumb mixture and sprinkle the tops with the breadcrumbs. Lightly press the breadcrumbs so they stick to the chicken. Don’t worry if the bottom is not as coated as well; you want most of the breadcrumbs to coat the top of the roll-ups so they get nice and crispy in the oven.
Place the roll-ups seam-side down in the prepared baking dish. If extra breadcrumbs are in the bowl, sprinkle them over the top of the roll-ups.
Bake the roll-ups for 20 to 30 minutes or until the internal temperature is 165°F. Let them rest in the baking dish for a few minutes before serving. Sprinkle the parsley over the top if using.
Notes
Some cheese may ooze out when you bake the rolls. You don't want all of it oozing out, so keep the cheese mainly in the center of the ham, leaving an edge when you assemble the roll-ups. That way, the cheese stays inside when you roll up the chicken. You can use toothpicks to secure the roll-ups - just remember to remove them before slicing the rolls.