1. Mince 2/3 of chiles; put in a mortar with garlic and sugar and pound into a coarse, wet paste.
2. Transfer chile mixture to a small bowl and add 2/3 cup warm water, lime juice, and fish sauce. Stir well to dissolve. Add reserved chiles and carrot and set aside at least 10 minutes and up to 3 hours before serving.
Note: Nutritional analysis is per Tbsp.