Place grated carrots in a large bowl.
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.
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.
I usually double this recipe, as a large bag of carrots yields lots of salad.
Using tamarind is the traditional method; however it is hard to find in regular grocery stores. Any Asian grocery store/market will have it. Lime juice makes a reasonably good substitution.
The amounts of Thai red curry paste and red pepper flakes can be increased to suit your taste (it is Thai food after all).
The dressing is very similar to one of the dipping sauces usually served with Thai spring rolls, so the dressing can be made on its own for that purpose. I have also used this as a dressing for a thin sliced cabbage slaw.
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