Heat olive oil in a large skillet over medium heat.
Season the chicken breasts with salt and pepper, then place them in the skillet.
Cook the chicken for about 6-7 minutes per side, or until cooked through.
Remove the chicken from the skillet and set it aside on a plate.
In the same skillet, add chopped onion and garlic; sauté until softened.
Stir in the fresh spinach and cook until wilted.
Pour in the chicken broth and heavy cream, stirring to combine.
Season the sauce with Italian herbs, salt, and pepper to taste.
Return the chicken to the skillet, spooning sauce over each piece.
Serve the chicken garnished with grated Parmesan cheese.