I would say "the purple fork" and "Peel" are my favorite in my style inspiration.
in Korean cultural, we use spoon not fork and knife. also I really don't want any designs inspired by Korean flag.
here is my idea,
-similar concept as "The purple fork" logo but design with spoon and get inspiration from the Korean dish called Bibimbap(please research on google) or the top two pictures on the contest attachment. such as colors and designs
-similar concept as "Peel" logo, but use spoon.