both Korean BL mini series
while The Director who buys me dinner only is has flash backs to historical settings Nobleman Ryu’s Wedding only takes place in the Joseon period.

LGBT+ themes as well as a cooking/food aspect

Eating around other people is a struggle for salaryman Yutaka, despite his talent for cooking. All that changes when he meets Minoru and Tane—two brothers, many years apart in age—who ask him to teach them how to make his delicious food! Yutaka soon finds himself having a change of heart as he looks forward to the meals they share together.