Heat olive oil in a large skillet over medium-high heat.
Add the chicken pieces to the skillet and cook for 5-6 minutes, stirring occasionally, until golden brown and cooked through. Remove chicken from the skillet and set aside.
In the same skillet, add the diced onion and cook for 2-3 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the diced red bell pepper, zucchini, and sliced mushrooms to the skillet. Cook for 5-6 minutes, stirring occasionally, until the vegetables are tender.
Return the cooked chicken to the skillet and stir to combine with the vegetables.
Pour in the chicken broth and bring to a simmer. Cook for 3-4 minutes to reduce slightly.
Reduce heat to medium-low and stir in the heavy cream, grated Parmesan cheese, dried Italian seasoning, salt, black pepper, and crushed red pepper flakes.
Cook for an additional 5 minutes, stirring occasionally, until the sauce thickens and coats the chicken and vegetables.
Add the baby spinach leaves and cook for 1-2 minutes until wilted.
Remove from heat and sprinkle with chopped fresh parsley before serving.