Preheat oven to 400 degrees F. Coat a 13- x 9-inch baking dish with nonstick cooking spray.
Heat the olive oil in a large nonstick skillet over MEDIUM-HIGH heat. Add the chicken to the pan. Season with ½ teaspoon salt and the garlic pepper. Cook, stirring occasionally, until well browned, about 6 to 8 minutes. Transfer the chicken to a medium bowl. Add the remaining 2 teaspoons of oil to the pan and return it to the heat. Add the zucchini, bell pepper and garlic and cook, stirring occasionally, until the vegetables are just barely fork tender, about 4 minutes. Transfer the zucchini mixture to the bowl with the chicken and set aside.
Add the butter to the pan. Stir in the flour and cook, stirring constantly, until the flour starts to brown, about 1 minute. Whisk in the broth and milk. Bring to a low boil, whisking often to smooth out the sauce as much as possible (a few small lumps are okay). Remove from the heat and add the cream cheese, ¾ cup mozzarella and 2 tablespoons Parmesan and stir until melted. Stir in the remaining ½ teaspoon salt and the black pepper.
Drain all of the liquid from the chicken and vegetable mixture and stir the mixture into the cheese sauce in the pan. Transfer the mixture to the prepared baking dish. Sprinkle the casserole with the remaining ½ cup mozzarella, remaining 2 tablespoons Parmesan, and the breadcrumbs.
Bake until the top is browned and the edges are bubbly, 20 to 25 minutes.If desired, set the oven to BROIL for the last minute of the cooking time to brown the top a little more. Remove from the oven and let it rest for 10 minutes before serving.