Combine 2 1/2 cups boiling water and tamarind in a large bowl; let stand 10 minutes. Break tamarind into small pieces; let stand 5 minutes. Strain mixture through a sieve over a bowl, reserving liquid; discard solids.
Combine 1/2 cup sugar and 1/2 cup water in a microwave-safe dish; microwave at HIGH for 2 minutes or until sugar dissolves, stirring once. Cool. Combine tamarind liquid, sugar syrup, vodka, and juice in a pitcher, stirring well. Add crushed ice; stir or shake well. Garnish rims of 8 martini glasses with sugar, if desired. Strain chilled martini mixture into prepared glasses; garnish with lime wedges, if desired.
Made to recipe proportions using tamarind nectar. Rather than plain sugar, coated one-half-side of each rim with sugar/salt mixture (4tsp dark sugar, 4tsp kosher salt, 2tsp cinnamon, 1tsp cayenne). We love tamarind and liked the drink, but no way should this be called a martini.