Add potatoes to a pan of very salty water. The potatoes should float in the water. If they don't, add more salt. Bring to a boil; simmer about 25 minutes. Drain off most of the water; reduce heat to allow any liquid to evaporate. shake pan to enable salt to crystallize. Turn off heat, cover potatoes with a tea towel about fiver minutes to enable potatoes to dry and turn "wrinkly".
Cover the chilies in boiling water and let them soak for an hour. Place all the ingredients except the olive oil into a food processor to form a paste. Slowly drizzle in the olive oil with the motor running. Wipe some of the salt off the potatoes and serve with the sauce in small bowls.