Add all the ingredients into a shaker with ice and shake.
Double-strain into a Martini glass.
Garnish with guava fruit leather (or piece of guava paste).
*Guava syrup: Slice 1 1/4 cup guava and macerate with 1 1/4 cup sugar and 3/4 cup water, mixing occasionally until the sugar is dissolved. Refrigerate the mixture until ready to strain. (Ideally, this can be done 1 day in advance and left overnight in the fridge.) Strain the syrup from the pulp, keeping the pulp for garnish if you wish.
**Guava fruit leather: Take the discarded guava pulp, and mix in a blender until smooth. Pour mixture through a large sieve and spread over a piece of parchment paper to make an even. Place sheet in an oven set at 135 degrees F for about 6 hours, checking periodically to prevent overdrying. Remove and cut into 1 x 2 inch slices.