Preheat oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.
In a bowl, mix together sour cream, mayonnaise, garlic powder, salt, pepper, and Parmesan cheese until well combined.
Cut chicken breasts in half lengthwise to create thinner cutlets.
Roll out the crescent roll dough and place a piece of chicken on each triangle. Spoon the cream mixture over the chicken.
Sprinkle shredded mozzarella on top of each.
Roll up each crescent and place in the prepared baking dish.
Bake uncovered for 25-30 minutes, or until the chicken is cooked through and the tops are golden brown.
Garnish with fresh parsley before serving, if desired.