Preheat oven to 375°F. Grease a 9 x 13 or similar size baking dish.
Use a sharp knife to slice thick chicken breasts in half lengthwise, to make 6 cutlets. Place chicken breasts in single layer in the bottom of baking pan.
In a small bowl, combine the mayonnaise, sour cream, 1/4 cup of the parmesan cheese, salt, pepper, parsley, thyme and garlic. Spread evenly over each chicken breast.
Top each breast with mozzarella cheese and remaining 1/4 cup parmesan cheese.
Bake for 1 hour, until cheese is crisp and chicken is at least 165°F on instant read thermometer. Let chicken rest for 5 minutes before serving.