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1
Combine the tamarind paste with 1/2 cup very hot water and break up the paste with a spoon or your fingers; soak for a few minutes, breaking up the paste a few more times if needed. Push the mixture through a mesh strainer with the back of a spoon; set aside the pulp that passes through the strainer, and discard what remains inside the strainer. Stem and seed the chiles.
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2
Heat the oil in a wok or large skillet over medium-high heat until hot but not quite smoking. Add the chiles, and cook, stirring, for 15 to 20 seconds, making sure they don't burn. Remove with a slotted spoon, and transfer to a plate.
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3
Add the garlic to the oil, and fry, stirring frequently, until just golden brown. (It will continue to brown after it's out of the oil, so don't go too dark now.) Transfer to the plate with the chiles. Fry the shallots until golden brown, and transfer to the plate. Turn off the heat, leaving the oil in the pan. Transfer the chiles, garlic, and shallots to a food processor; pulse, scraping down the sides as necessary, until the mixture turns into a paste (no need to make it totally smooth).
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4
Turn the heat under the pan to medium. Add the shrimp paste, and cook, stirring and breaking it up, for about a minute or two. Add the palm sugar, and cook, stirring, until it dissolves. Add the chile, garlic, and shallot mixture, the tamarind pulp, and 2 tablespoons of the fish sauce. Stir to combine, then turn the heat to low. Cook, stirring occasionally so the bottom of the pan doesn't burn, until the mixture thickens slightly, 2 or 3 minutes. Taste the mixture; if it still needs salt, add more fish sauce, a little at a time.
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5
You can store the jam (and the oil) in a jar in the fridge or freezer; use it in stir fries or soups, spoon it on top of rice or noodles, spread it on toast, or use it as the base for the dressing for Yum Yai Salad: https://food52.com/recipes/37432-yum-yai-salad.
