The ramen at this shop has a good old-fashioned taste.
yearn for; miss; feel nostalgic about
show nostalgia for; long for; reminisce fondly about
Bound form of the adjective 懐かしい (natsukashii), used in classical or fixed expressions. The exact historical derivation is uncertain, but it is related to the verb 懐く (natsuku, 'to become attached to').