"To complement the dish" means to add something that enhances or completes the flavors and presentation of the food. It is like adding a special ingredient or side dish that goes well with the main food item and makes it better. Full definition
It's heavy on tropical fruit and citrus, which complements the dish's savory flavors and rich acidity. (the-broken-bread.com)
Our extensive wine list and beer menu complements any dish. (marigoldmaison.com)
This eatery boasts a superb range of Italian specialities, including homemade pasta and pizza which is served alongside local wine which complements each dish perfectly. (holiday-weather.com)