For persimmon purée:
2 non-astringent persimmons, such as Fuyu
1/2 to 1 ounce cardamom simple syrup, to taste
For the cocktail:
1 1/2 ounce persimmon purée
1 ounce freshly squeezed lime juice
1 3/4 ounces gin
First, make a persimmon purée by blending two persimmons—stem removed—with 1/2 to 1 ounce simple syrup (to taste) in a blender. To make simple syrup, use equal parts sugar and water with three cardamom seeds, bring to a boil and cool.
In a cocktail shaker filled with ice, combine 1 1/2 ounces persimmon purée, with gin and lime juice. Shake for 15 seconds.
Strain into a glass and garnish with a lime slice.