Heat olive oil in your largest pot over medium-high heat. Once shimmering, add the chicken pieces and cook for 4-5 minutes per side until golden brown on the outside (the chicken doesn't need to be cooked through yet). Remove chicken and set aside on a clean plate.
In the same pot, add diced onion and cook for 2-3 minutes until softened and fragrant. Then add minced garlic and cook for another 30 seconds, stirring constantly to prevent burning and to build a flavorful aromatic base.
Return the chicken to the pot and pour in the chicken broth. Add bay leaves and Italian seasoning, then bring everything to a gentle boil. Reduce heat to medium and simmer for 10 minutes to allow the chicken to finish cooking through completely.
Stir in the uncooked pasta directly into the pot along with the diced tomatoes. Make sure the cozy one pot chicken pasta gets evenly distributed throughout the liquid. Simmer for 12-15 minutes, stirring occasionally to prevent sticking and to ensure even cooking.
Add the sliced mushrooms and fresh spinach, stirring until the spinach wilts completely into the pot. Then pour in the heavy cream and stir everything together gently.
Remove from heat and stir in the grated Parmesan cheese. Season with additional salt and black pepper to taste, then let it rest for 2-3 minutes before serving to allow flavors to meld beautifully.