In a non-aluminum saucepan, combine the vinegars, corn syrup, fish sauce along with four tablespoons of water. Bring to a boil and stir. Remove from heat and let mixture cool to room temperature. In a food processor, combine the garlic, chilis and sugar and quickly puree. Add the cooled syrup and process in one or two bursts just to combine. Add basil and briefly process until basil is minced. Store in a covered container in the refrigerator for up to one week.