Grate the carrots coarsely and place them in a large bowl.

In a saucepan, combine sugar, water, and rice vinegar.

Bring the mixture to a boil and cook until the sugar dissolves, about 5 minutes.

Reduce the heat to medium, and add garlic, fish sauce, and red curry paste to the sugar mixture.

Simmer until the flavors blend, about 2 to 5 minutes.

Remove the saucepan from the heat and allow the dressing to cool completely, about 30 minutes.

Stir lime juice and red pepper flakes (if using) into the cooled dressing.

Pour the dressing over the grated carrots.

Add the chopped peanuts.

Toss to coat all ingredients evenly.

Refrigerate the salad until chilled, at least 30 minutes.