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To make the salad, thinly slice the cucumbers and spread them out a bit in a large colander. Sprinkle cucumbers with salt. Set the bowl in your sink and let the cucumbers drain for about 30 minutes.
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Once the cucumbers have drained for 30 minutes, press the cucumbers a bit to drain out as much water as you can and then spread them out on a towel and blot them dry.
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Put the drained and blotted cucumbers in a medium bowl and pour the prepared lime vinegar (see below) over the cucumbers. Sprinkle with most of the toasted black sesame seeds--reserving some seeds for the garnish. Toss the cucumbers and the vinegar syrup together and refrigerate the cucumbers until you are ready to serve.
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When you are ready to use the cucumbers either as a stand-alone salad or as a garnish, remove the cucumbers from the dish using a slotted spoon. Add the lime juice and stir the mixture together. Scatter the remaining toasted black sesame seeds over the cucumbers.
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To make the lime vinegar, heat the vinegar and sugar in a small saucepan just until the mixture begins to boil, stirring as you go. Lower the heat to a simmer and continue to cook for 2 to 3 more minutes. You want the sugar to be completely dissolved and you want the mixture to be a little syrupy.
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Remove the syrup from the heat and stir in lime zest and half of the lime juice. Cool a bit and taste the syrup. You can add more lime juice to your taste if you want. Cool the syrup completely before using on your sliced cucumbers.