Preheat the Oven - Set the oven rack to the lower-middle position. Preheat to 375ºF (191ºC).
Prepare the Mushrooms - Rinse and dry the mushrooms, or wipe the surface with a damp paper towel. Trim the stems and cut them into ¼-inch thick pieces. There should be about 2 ½ cups of sliced mushrooms.
Saute the Aromatics - Heat a large oven-proof skillet or wide dutch oven over medium-low heat. Add 1 tablespoon of olive oil. Once warm, add the shallots. Saute until translucent, about 1 to 2 minutes. Add 1 ½ teaspoon minced garlic and Italian seasoning, and saute for 30 seconds.
Saute the Mushrooms - Increase the heat to medium. Add the mushrooms, then sprinkle with ¼ teaspoon salt and ¼ teaspoon black pepper. Saute until they just start to release their moisture, occasionally stirring, about 2 to 3 minutes. Add the balsamic vinegar and soy sauce, stir and cook until most of the liquid evaporates, about 1 minute.
Saute the Spinach - Add the spinach to the pan and cook until wilted, about 1 minute. Transfer the mixture to a bowl to cool down slightly. Wipe the pan clean with paper towels or wash if needed.
Prepare the Chicken - Butterfly the chicken breast in half lengthwise, leaving about a ½-inch uncut area on the other side connected. Repeat with the remaining pieces.
Season the Meat - In a small bowl, combine 1 teaspoon salt and ½ teaspoon black pepper. Evenly season each side of the chicken with the mixture.
Stuff the Chicken - Inside each chicken breast, evenly divide the mushroom filling. Top with 1 tablespoon parmesan cheese and a slice of mozzarella, halved to fit if needed. Close the opening on the side with toothpicks to secure the filling.
Sear the Chicken - Heat the same pan used to cook the filling over medium heat. Once the pan is hot, add 2 tablespoons of olive oil. Add the chicken, presentation-side down, and lightly press the meat to make contact with the pan. Cook until golden-brown on the surface, about 5 minutes. Flip and cook for 3 minutes. If using smaller chicken breasts, check for doneness as baking may not be necessary.
Transfer to the Oven - Place the pan in the oven and bake until the meat is no longer pink and the internal temperature reaches 160 to 165ºF (71 to 74ºC), about 10 to 15 minutes, depending on the thickness. Transfer chicken to a clean plate, and cover with foil to keep warm. Leave the juices in the pan.
Make the Sauce - Heat the pan with the chicken juices over medium heat. Add 1 ½ teaspoon minced garlic, and saute for 30 seconds. Add the cream and continuously stir, scraping any browned bits on the bottom of the pan. Reduce the sauce until lightly thickened, about 2 to 3 minutes. Season with salt and pepper to taste. Stir in the chopped parsley.
To Serve - Remove the toothpicks from the chicken. Serve while still hot with the cream sauce.
Filling: Makes 1 cup of filling
Storing: Cool completely and store in an air-tight container for up to 5 days.
Reheating: Cover and reheat in the microwave on high heat in 15 to 30-second increments until hot.
Using Frozen Spinach: Defrost 2.5 ounces of frozen chopped spinach, about ¼ cup, and drain well. Stir the spinach in with the mushrooms.
Make it Gluten-Free: Use gluten-free tamari or coconut aminos instead of soy sauce.
Make Ahead: The filling can be made separately, 3 days in advance. The chicken can be stuffed, covered, and refrigerated for up to 3 days before cooking.
Baking Directions: Place stuffed chicken on a greased foil-lined sheet pan. Bake at 425ºF (218ºC) for about 20 to 25 minutes, depending on the thickness.