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.
In both dramas main character works as chef in present times and a mishap causes them to travel back in time and to survive during this unsettled times they uses their knowledge on fine cuisine