Heat the vegetable oil in a skillet over medium heat. Fry the chopped garlic, shallot, and chilies until fragrant and lightly golden, 2–3 minutes. Remove from heat.
Grind the roasted unsalted peanuts in a food processor or mortar to a coarse paste.
Add the fried aromatics and palm sugar to the peanuts and process or pound to a rough, cohesive paste.
Scrape the paste into a saucepan and add the tamarind paste, kecap manis, salt, and water. Bring to a gentle simmer over medium heat, stirring frequently.
Simmer 8–12 minutes, stirring often, until the sauce thickens to a spoon-coating consistency and a slight sheen of oil rises to the surface.
Stir in the lime juice. Taste and adjust salt if needed. Serve warm or at room temperature.