Combine coconut milk and curry paste in a small sauce pan over low-medium heat, whisking constantly as it begins to warm up.
When the mixture begins to simmer, whisk in peanut butter, brown sugar and fish sauce (or soy sauce / tamari).
Continue to simmer, whisking constantly, until the sauce thickens slightly and has a smooth consistency, about 4 minutes. (Note: If the sauce starts to boil or simmer vigourously, reduce the heat. Cooking the sauce over high heat can cause it to separate.)
Taste the sauce and adjust with extra sugar or fish sauce, if needed. Serve warm.
Peanut sauce will keep in the refrigerator for up to 3 weeks. Reheat it slightly before serving.