Preheat your oven to 375°F. In a large bowl, toss the cubed chicken with paprika, salt, and pepper until evenly coated.
Heat olive oil in a large skillet over medium heat. Add the seasoned chicken and cook for 4-5 minutes, until lightly browned (it doesn’t need to be fully cooked through). Remove from heat.
In a large mixing bowl, combine the onion, bell pepper, zucchini, yellow squash, eggplant, garlic, diced tomatoes, oregano, thyme, and a pinch of salt and pepper. Toss to mix.
Add the chicken to the vegetable mixture and stir to combine. Transfer everything to a greased 9x13-inch baking dish. Sprinkle the top evenly with mozzarella and parmesan cheese.
Bake for 25-30 minutes, until the vegetables are tender and the cheese is melted and bubbly.