Soak the tamarind pulp in 1/2 cup of hot water for 10-15 minutes. Once softened, mash the pulp with your hands to extract as much juice as possible.
Strain the tamarind pulp through a fine-mesh sieve to remove any seeds or fibers.
In a saucepan, combine the tamarind pulp, jaggery or brown sugar, cumin powder, red chili powder, salt, and 1/2 cup of water.
Cook the mixture over medium heat for 15-20 minutes, stirring occasionally, until the chutney thickens and the sugar has dissolved completely.
Remove the saucepan from heat and let the chutney cool to room temperature.
Transfer the chutney to an airtight container and store it in the refrigerator for up to a week.