Tear tamarind paste into chunks and add to a medium saucepan. Cover with 1 cup water and soy sauce. Simmer over low to medium heat for 5 minutes, then mash to extract the pulp.
Strain tamarind pulp over a bowl. Using a rubber spatula, push the pulp through the strainer, leaving behind the seeds, and stringy fibers to discard. Don't forget to scrape the pulp that collects on the bottom of the strainer!
Add vinegar, chili paste, salt, and ginger powder. Stir to blend ingredients. Clean the saucepan and pour the tamarind mixture back into it. Stir brown sugar into the tamarind mixture; simmer for a few minutes over low heat to dissolve the sugar.
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Notes
If the Soy Tamarind Sauce is too thick, add water, 1 tablespoon at a time, until you achieve the desired consistency.
To store Soy Tamarind Sauce leftovers, pour into an airtight container and store in the refrigerator. It should be good for a few weeks, as long as there is no cross-contamination.