If you've never had the lychee fruit, you're missing one of the edible joys of life. I've had the good fortune to travel to various countries in Southeast Asia, specifically Thailand, Singapore, Cambodia, and Vietnam. I had a great time, as well as some amazing cocktails and liquors. None of those countries is a major producer of lychee (China is the big one), but you can find it on many menus.
There are some lychee liquors on the market, so if you can get one, making this cocktail is easy.
2 ounces vodka (I'm a big fan of Zyr)
1 ounce Soho lychee liqueur
.25 ounces super simple syrup
Combine in shaker, stir with the dynamic energy on the streets in Bangkok and Saigon, and strain into a chilled cocktail glass.
Soho makes a very good liqueur that has a solid lychee taste and is vaguely sweet. I've made this cocktail with Chinese lychee liqueurs that I found in San Francisco, but they were pretty bitter and so were the resulting cocktails. If this recipe is too sweet for you, forget the simple syrup or add vodka. If the lychee taste is too strong, then add a little more vodka, simple syrup, or both.
This cocktail brings back memories such as haggling in Thai with vendors in Bangkok, walking through the almost unreal beauty of the National Botanical Garden in Singapore, watching a gorgeous sunrise on the beach in Nha Trang, and riding an elephant near the majestic ruins of Angkor Wat. I hope you will associate this cocktail with your own great experiences.