Step 1

Place grated carrots in a large bowl.

Step 2

Combine sugar, water, and vinegar in a saucepan and bring to a boil; cook until sugar is dissolved, about 5 minutes. Reduce heat to medium; add garlic, fish sauce, and curry paste to sugar mixture and simmer until flavors blend, 2 to 5 minutes. Remove saucepan from heat and cool dressing completely, about 30 minutes.

Step 3

Stir lime juice and red pepper flakes into dressing and pour over carrots. Add peanuts and toss to coat. Refrigerate until chilled, at least 30 minutes.