Make tamarind paste: remove the hard outer shell and stringy bits from tamarind pods. Place in a bowl, cover with 1 cup hot water, and soak 1½ hours. Transfer tamarind to a fine mesh sieve set over the soaking water; press the pulp through the sieve, separating it from the black seeds. Discard seeds and whisk pulp with the soaking water. Refrigerate until needed.
Fill a shaker with ice and add all liquid ingredients.