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1
Combine the tamarind and 4 cups water in a medium-size heavy saucepan set over medium-high heat, and bring to a boil.
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2
Boil, uncovered, until the tamarind is very soft, 10 to 15 minutes.
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3
Carefully pour the water into a container and set it aside.
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4
Using a potato masher, mash the tamarind in the saucepan (the seeds are still in there).
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5
Return the reserved tamarind water to the saucepan and mix it into the mashed pulp.
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6
Then strain the mixture into a pitcher, pressing on the solids to extract as much liquid as possible.
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7
(Discard the solids.)
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8
Stir in 3 cups fresh water (the mixture should be fairly concentrated).
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9
Add the sugar and stir until it is dissolved.
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10
(The tamarind water can be made 2 days ahead and refrigerated.)
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11
Put the chile-lime powder on a small plate.
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12
Using the lime wedge, moisten the rims of 6 martini glasses.
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13
Invert the martini glasses into the powder on the plate to coat the rims.
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14
Turn the glasses right side up and put 1 salted plum in each glass.
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15
Set aside.
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16
For each serving, combine 3/4 cup tamarind water and 1/4 cup vodka in a cocktail shaker with ice.
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17
Shake vigorously.
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18
Strain into a prepared martini glass and serve.
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19
(Alternatively, you can mix all the tamarind water, all the vodka, and some ice in a large pitcher and just pour the mixture into each martini glass for a faster preparation.)
