Toss the cucumber, vinegar, sugar and 2 teaspoons salt in a medium bowl and set aside at room temperature, tossing occasionally, until juicy, about 30 minutes.
Meanwhile, put the almonds in a large skillet and heat over medium, swirling them around until golden and toasted in spots, about 3 minutes. Set aside to cool.
Add the oil and garlic, the cucumber mixture along with any collected juices, 6 ice cubes and all but 2 tablespoons each of the almonds and parsley to a blender. Blend on high until very smooth. Refrigerate until chilled, about 2 hours.
Pour into 2-ounce shot glasses. Sprinkle each with the reserved almonds and parsley.
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