Heat the olive oil in a large skillet or sauté pan over medium-high heat. Add the chicken pieces and cook until browned on all sides, about 5-7 minutes. Remove the chicken from the skillet and set aside.
Add the chopped onion to the skillet and cook until softened, about 3-4 minutes. Stir in the minced garlic and cook for another minute until fragrant.
Add the chopped red bell pepper and broccoli florets to the skillet. Cook for 5 minutes, stirring occasionally, until the vegetables are tender-crisp.
Return the browned chicken to the skillet. Stir in the undrained diced tomatoes, chicken broth, Italian seasoning, salt, and pepper.
Bring the mixture to a simmer, then reduce the heat to low, cover, and cook for 10-15 minutes, or until the chicken is cooked through and the sauce has thickened slightly.
Taste and adjust seasoning if necessary. Serve hot, garnished with grated Parmesan cheese (if using) and fresh parsley.