Tokyo Martini
There are several drinks by this name around the web. The others are poor imitations, please disregard.
You'll need a green tea bitter: Vodka in which some green tea leaves have been steeped for a while. I prefer darjeeling leaves for a day, perhaps even briefer.
Make as a very dry martini with a few drops of the green tea bitter, and a thin slice of ginger. Enjoy.
I'm not sure which martini variant I like better, the Webster F. Street layaway plan or this? Try both.