Here's the step that takes the Marry Me Chicken sauce from good to glossy, restaurant-level rich.
Once the sauce has simmered and thickened, take the pan off the heat and swirl in 1 tablespoon of cold butter until it melts and emulsifies. This classic restaurant move (called "mounting" the sauce) gives it a glossy sheen and velvety body you can't get from cream alone.
Deglaze first for extra depth: after searing the chicken, add a splash of the broth and scrape up every browned bit stuck to the pan before building the sauce — that fond is pure flavor.
Bonus: a small squeeze of lemon right at the end brightens the whole dish and cuts the richness.