Prep. Preheat oven to 400˚F and lightly grease a 9x13 baking dish with cooking spray. Set aside.
Brown the chicken. Add olive oil to a 12-inch skillet and set over medium-high heat. Add diced chicken to the pan; cook, stirring occasionally, for about 8 minutes or until the chicken is browned and cooked through. Transfer the chicken to a bowl and set aside.
Cook the vegetables. Add zucchini and bell peppers to the same pan; cook, stirring occasionally, for about 4 minutes, or until the vegetables are just tender. Add garlic and cook for 20 seconds. Stir in the corn and cook for 1 minute, or until heated through. Transfer the zucchini mixture to the bowl with the chicken. Set aside.
Make the sauce. Add butter to the same pan and melt. Stir in the flour and cook, stirring constantly, until the flour starts to brown, about 1 minute. Whisk in the broth and half & half and bring it to a boil, whisking often. Remove from heat; stir in the cream cheese and 3/4 cup mozzarella; continue to whisk and stir until melted. Season with salt and pepper.
Combine. Drain the liquid from the chicken and vegetable mixture. Stir the chicken and vegetables into the cheese sauce. Transfer the chicken and veggies to the prepared baking dish.
Bake. Sprinkle the top of the casserole with the remaining mozzarella cheese and bake for 22 to 25 minutes, or until the edges are bubbly and the top is browned. Remove from oven and let the casserole rest for 10 minutes.
Finish and serve. Taste the chicken zucchini casserole for salt and pepper and adjust accordingly. Garnish with parsley and serve.