Remove the hard shells from tamarind pods and discard them, leaving about 1 cup of pulp.

Bring 6 cups of water to a rolling boil in a large pot over high heat.

Stir the tamarind pulp into the boiling water until the liquid turns a rich brown color.

Reduce heat to medium and simmer for 3 to 5 minutes, stirring occasionally to extract maximum flavor.

Strain the mixture through a fine mesh strainer lined with cheesecloth into a bowl, pressing gently on the pulp to extract all liquid.

While the liquid is still warm, stir in 1/3 cup sugar and 1/4 teaspoon salt until completely dissolved.

Let the mixture cool to room temperature, then transfer to a glass pitcher and refrigerate for at least 30 minutes until cold.

Serve over ice cubes and garnish with fresh lime wedges, if desired.