In a food processor, whirl peanuts, garlic, chili, galangal, and sugar until finely ground.
In a 2- to 3-quart pan over high heat, combine peanut mixture, coconut milk, and sweet soy sauce. Bring to a boil, stirring constantly. Reduce heat and simmer, uncovered, stirring occasionally, until sauce is slightly darker and thicker, about 15 minutes. Add lime juice and salt to taste. Serve warm or at room temperature.
Nutritional analysis per tablespoon.