How does one say 'my compliments to the chef'?

Question

What is the expression 'compliments to the chef' or 'give my compliments to the chef' in Japanese?

Is there a suitable matching phrase, or something that expresses a similar message?

(Please answer with as much English and Romaji as possible)

Answer 1

You haven't given any concrete context, but ご馳走様でした gochisōsama deshita is a very common phrase conveying that it was a very good meal. You can/should use this phrase if you are talking to the chef (or you can say it loudly if you pass by the kitchen on the way to the counter where you pay after your meal). However, telling it to the waiting staff, the message is unlikely to get passed on to the chef, since it's a very common phrase to thank someone for the meal.

For more on the meaning of this phrase see

• About ご[馳走]{ちそう}: two “runs” would give you “a feast”?
• Etymology of ごちそうさまでした

Answer 2

ご馳走様でした gochisōsama deshita is a common phrase, but it is more of "thank you for the meal" so it may be too general to express your compliment to the chef.

Some type of Japanese eateries have chefs in the front of the restaurant and they may even be serving the dishes to you as they cook. Then you can directly say ご馳走様でした gochisōsama deshita to the chef and maybe add とてもおいしかったです！ (totemo oishikatta desu!) that would make the chef give you a smile.

As you say とてもおいしかったです！to the server, some izakaya-style eateries may convey your message to the entire restaurant by shouting お客様からおいしかったですをいただきました！ (okyaku-sama kara oishikatta-desu wo itadakimashita!) then you will know the entire restaurant staff know you enjoyed the meal.