In Ginza, where the streets are wide and the people polished, you’ll find Higashiya Ginza—a shop and teahouse that makes fine wagashi, the refined confectionery that accompanies green tea in Japan. (The name Higashiya means “daily sweetshop.”)

Each morsel offers no more than a few mouthfuls, though the diminutive bamboo picks with which they are served allow diners to stretch out the experience with tiny birdlike bites. In the adjoining café, diners can sample a wagashi flight with tea or liquor pairings. The confections change seasonally, but may include yuzu domyojikan, using citrus rind, agar and mochi rice; or the natsume butter sweet, which combines fermented butter, walnuts and date palm sugar.

The shop’s design is the work of Shinichiro Ogata of Simplicity, and is as sop...