Preheat the oven to 375°F (190°C).
In a large bowl, combine the diced zucchini, sweet onion, 1 tablespoon olive oil, half the paprika, salt, and pepper. Toss until evenly coated.
In another bowl, season the chicken pieces with the remaining paprika, salt, pepper, and cornstarch. Toss well to coat.
Heat the remaining tablespoon of olive oil in a large skillet over medium heat.
Add the chicken in a single layer and cook for 3–4 minutes, turning once until lightly golden but not fully cooked.
Pour in the chicken broth and scrape up any browned bits from the pan.
Spread the seasoned zucchini and onion mixture into a baking dish.
Pour the partially cooked chicken and broth evenly over the vegetables.
Sprinkle the Monterey Jack and Parmesan cheeses over the top.
Cover tightly with aluminum foil.
Bake for 25 minutes.
Remove the foil, stir gently, and continue baking uncovered for another 10–15 minutes until the cheese is lightly golden and the chicken is fully cooked.
Stir gently before serving your delicious Chicken Zucchini Bake.