Add the cucumber chunks to the bowl of a food processor. Puree until the cucumbers have broken down into a smooth mixture. Strain the processed cucumbers over a medium bowl. Clean the strainer. Get another medium bowl and strain the cucumber juice again. Strain one last time (cleaning the strainer in between each time you strain) into a clean glass. The mixture should be clear by the third time you strain. If it’s still pretty cloudy, repeat the straining process until it’s clear. You should end up with 1 cup of fresh cucumber juice.

Fill a martini shaker with ice and add the vodka, lime juice, and 2 oz of the fresh cucumber juice. Shake vigorously and strain into two martini glasses. Serve immediately.

The remaining fresh cucumber can be reserved in the refrigerator for up to 5 days.