Reduce the heat to low. Add the remaining 1 tablespoon unsalted butter, garlic, chicken, and any accumulated juices on the plate to the skillet. Cook until the butter melts and the garlic is fragrant, about 1 minute. Remove the skillet from the heat, add the Parmesan cheese, and toss to coat. Garnish with the parsley, more Parmesan cheese, and red pepper flakes if desired.
