- Make a simple syrup by placing the water and sugar into a small sauce pan. Add the jalapeño half to the sugar water and bring to simmer. Stir until sugar is dissolved, then remove from heat. Refrigerate until needed.
- Remove the outer green peel from the watermelon rinds with a vegetable peeler and discard. Dice the rind and add it to a blender along with the cucumber. Puree.
- Pour the mixture through a fine mesh strainer set over a bowl. Discard pulp and add the juice back to the blender.
- Add the simple syrup from step one to the blender along with the triple sec and the mint. Squeeze in the juice from the lime and blend well.
- Fill 2 highball glasses with ice. Pour the mixture evenly into each glass, then top with prosecco. Garnish with watermelon wedges, jalapeno slices, and mint sprigs.