Heat olive oil in a large deep skillet or Dutch oven over medium heat.
Season the chicken breasts evenly with salt, black pepper, and dried Italian seasoning on both sides.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side until golden brown and cooked through (internal temperature 165°F). Remove chicken from the skillet and set aside.
In the same skillet, add the diced onion and minced garlic. Sauté for 2-3 minutes until the onion is translucent and garlic is fragrant.
Add the sliced zucchini to the skillet and cook for 4-5 minutes, stirring occasionally, until zucchini starts to soften.
Pour in the chicken broth and stir to combine, scraping up any browned bits from the bottom of the skillet.
Return the cooked chicken breasts to the skillet, nestling them into the zucchini mixture.
Cover the skillet and simmer on low heat for 5 minutes to allow flavors to meld and zucchini to become tender.
Remove the lid and sprinkle the grated Parmesan cheese evenly over the chicken and zucchini.
Cook uncovered for an additional 2 minutes until the cheese melts slightly.
Garnish with chopped fresh parsley before serving.