Slice chicken breast and half lengthwise. Similar to how you would butterfly a chicken breast except go all the way through creating two equal pieces per breast.
Season with salt and pepper.
Heat oil in a large sauté pan. Once hot, add chicken breasts and sear until brown, about four minutes per side. Reduce heat to medium-low and allow to cook all the way through. It should only take another minute or so.
Set cooked chicken breasts on a plate to the side. In the same pan add butter and flour. Whisk well to combine cook for one to two minutes.
Stir in marsala wine to create sauce. After a few minutes, add in heavy cream. If the sauce is too thick, add additional wine or a dash of chicken broth. Turn heat to low.
In a separate sauté pan, melt 1 tablespoon of butter, add sliced mushrooms and minced garlic. Sauté for five minutes, stirring often.
Once cooked, add prepared mushrooms to the prepared marsala sauce and stir to combine.
While the mushrooms are cooking, create your cheese filling. In a medium sized mixing bowl, add breadcrumbs, sour cream, shredded Gouda, shredded mozzarella, shredded Parmesan, sliced green onions, chopped sun-dried tomatoes, chopped parsley, and stir to combine.
Divide cheese mixture between two of the chicken breasts spreading across the top. Place corresponding sized chicken breast on top creating a sandwich. You may have extra cheese filling, depending on how much you use and how big your chicken breasts are.
Turn oven on to the broil function on High. Place stuffed chicken breasts in an oven safe pan and broil at high heat for 6 to 8 minutes until the cheese mixture has melted.
Plate and top with marsala sauce.