Preheat oven to 425 degrees F. Spray a 9x13-inch baking dish with nonstick cooking spray; set aside. Heat olive oil in a large skillet over medium-high heat.
Combine bread crumbs, parmesan cheese, salt, pepper, garlic powder and onion powder in a shallow dish or bowl; set aside. Whisk together eggs in a separate shallow dish or bowl; set aside.
Cut chicken breasts in half lengthwise or pound until 1⁄2- inch thick. Dip each piece of chicken in egg wash then coat in crumb mixture and place in skillet, cooking for 1-2 minutes on each side or until golden brown.
Remove chicken from skillet and place in prepared baking dish. Bake for 18 minutes, or until chicken is cooked through and lightly golden brown on top.
Remove from oven and top with ham and cheese and return to the oven and bake for an additional 3-5 minutes, or until cheese is melted.
In a small mixing bowl, whisk together all dip ingredients and serve with chicken.