A Boy and His Samurai (2010)

Both have a male character who time-travels and interacts with a female lead from modern day Korea/Japan.

They both have to do with time travel and romance.

They both involve time travel between eras and creating food! Chonmage Purina is a samurai who travels forward in time and makes his name by making pastries. Nobunaga No Chef travels back in time, leading to the character making dishes for a powerful daimyo named Nobunaga Oda.

Both movies are about cooking/baking. Both movies are very similar.......................................................................................................................................................................

Also starring Nishikido Ryu, as a samurai, who timeslips into the present day, and has to get a job, and impacts the community.

Chonmage is another touching father and son story. Chonmage Purin tends to be more humorous and has a fantastical plot, while Like Father, Like Son takes a more somber approach to fatherhood and tends to be more realistic.