Between a few months to around up to a year ago, I started a series and I can remember what it was about but not the name. It was a yaoi anime/manga where the main character was a cook that couldn't fight (also I believe he was trapped in a game world.)
He (the cook) was challenged to a duel which the second lead (a prince, I believe) accepted and won. And by doing so became husband and wife in a sense.
If anyone knows what this series is please help, it has been consistently at the back of my mind lately.
God save our King! has a similar setting to the one you've described. It has an anime adaptation too. However in this one the MC isn't a cook but they do duel after a fight at the dinner table and the MC accidentally proposes to the third prince.