First you will need to simmer the coconut milk in a large 12” nonstick skillet over medium-low heat for about 15 minutes. While it is simmering, make the flavoring paste by whizzing all the ingredients together in a food processor, adding a few tablespoons of water if necessary to keep the mixture moving. Add the flavoring paste to the simmering coconut milk, along with the daun salam and basil. Continue simmering the mixture, stirring occasionally, until it is reduced to half its original volume, about 45 minutes. While it is simmering, scrub the potatoes and slit each one half way through to help the flavors penetrate. Do not peel the potatoes as this will cause them to disintegrate from the long cooking.
When the coconut milk mixture is reduced, add the potatoes and salt, and continue cooking the mixture, stirring often to prevent sticking. Cover the potatoes and cook for about 10 minutes to make sure they cook through. Continue this until the liquid has dried up completely and the fat is rendered out. Add some peanut oil to the pan, if necessary, to have a total of 2 tablespoons of oil in the pan.
Turn the heat down to low and brown the potatoes and aromatics in the oil until medium-dark brown, about 20-25 minutes. The finished dish should be quite dry. Transfer the potatoes and the sautéed flavoring paste to a serving dish. Allow to rest for at least 30 minutes before serving.