Prepare the sauce: Mix together the milk, chicken broth, mustard, and cornstarch in a small bowl or cup. Set aside.
Prepare the chicken: Heat the oven to 400°F.
Lay the chicken pieces out on a work surface cut side up. Season with salt and pepper. Lay ½ slice of ham on each piece, then top with the cheese. Working from the smaller end, roll the meat and cheese up into the chicken. Place, seam side down in a baking dish that has been lightly oiled. (use a baking dish that will just hold the pieces of chicken snugly). Pour about ¼ cup chicken stock into the bottom of the pan, then place in the oven to bake. Bake until cooked through, about 20 minutes. Remove from the oven and set aside.
Prepare the Bread Crumb Topping: Heat the butter and oil together in a small sauté pan over medium heat. When hot, add the panko and cook, stirring constantly until they are golden brown. Remove from heat and set aside.
When the chicken is almost done, give the sauce a good mix, and then put it into a small saucepan, bring to a simmer, stirring. After a few minutes, it will thicken into a sauce; taste and add salt and pepper if needed. If the sauce gets too thick, add a little additional milk or stock.
To ServePlace one or two of the rolls onto a plate (you can slice them for presentation if desired). Top with the sauce and sprinkle the breadcrumbs over. Serve hot.