In Uji, Kyoto, the dish you are describing is a local specialty called Matcha Gyoza (Uji Matcha Dumplings). It is a unique savory twist on the city's famous tea culture.

Where to Find It

Two main shops on the Byodoin Omotesando path are famous for this:

1. Kyoto Uji TakoQ (蛸Q):

   • The Dish: Green-skinned dumplings infused with matcha.

   • The Experience: They are served with a small side of Matcha Salt (a blend of fine salt and matcha powder) for dipping.

   • Style: Mostly take-out with some outdoor bench seating. They also serve Matcha Takoyaki with matcha mayonnaise.

2. Ramen Tanaka Kyu Shoten (田中九商店):

   • The Dish: "Uji Matcha Gyoza."

   • The Experience: Like TakoQ, they serve their gyoza with matcha salt to enhance the earthy aroma of the tea.

   • Style: A sit-down restaurant where you can pair the dumplings with Matcha Ramen.