Line a 12x15 inch pan with parchment paper.
Place the tamarind pulp in a small bowl with 1/2 cup of hot water and let sit for 15-20 minutes. When the pulp-water mixture is cool enough to handle, break up the pulp in the water with your fingers, squishing it until the pulp breaks apart. You will probably also find some tamarind seeds in the pulp. Push the tamarind pulp mixture through a small sieve into another small bowl. You will end up with about 1/2 cup tamarind paste.
In a 5-quart to 7-quart pot, combine tamarind paste, sugar, brown sugar, corn syrup, cayenne pepper, salt, nuoc mam (fish sauce) (optional), evaporated milk, heavy whipping cream, and butter. Monitor the heat of the mixture with a candy thermometer while stirring. When the thermometer reaches 250 degrees F, remove the pot from the heat.
Stir in vanilla extract. Transfer mixture to the parchment-lined pan, let the mixture cool completely, and refrigerate. When cooled, cut the caramel into small squares and wrap the squares in parchment paper for storage.