Cut 2 1/2 inches off both ends of the cucumber. Reserve.
Peel middle sections, cut in half lengthwise, and use a spoon to scrape out seeds. Discard seeds.
In a blender, puree the middle sections of the cucumbers along with the garlic, shallot, jalapeño, mint and lime juice.
Strain through a fine strainer.
Stir in oil and vinegar.
Refrigerate for a minimum of 30 minutes.
Take reserved cucumber ends and slice off bottom 1/4 inch so that they can stand solidly on their ends. Use a zester or pairing knife to create designs in the peel, then use a small melon baller to scoop out most of the cucumber, creating a cucumber shooter glass.
Serve the chilled cucumber gazpacho in the shooter glasses.