Place 450 grams of grated carrots in a large bowl.
In a saucepan, combine 1 cup of white sugar, 1/2 cup of water, and 1/2 cup of rice vinegar.
Bring the mixture to a boil and cook until the sugar is dissolved, about 5 minutes.
Reduce heat to medium, add 2 tablespoons of minced garlic, 2 tablespoons of Thai fish sauce, and 1 1/2 teaspoons of Thai red curry paste to the sugar mixture.
Simmer until flavors blend, 2 to 5 minutes.
Remove saucepan from heat and let the dressing cool completely, about 30 minutes.
Stir 2 tablespoons of lime juice and 1 tablespoon of red pepper flakes into the dressing.
Pour the dressing over the grated carrots.
Add 1/2 cup of chopped unsalted peanuts and toss to coat.
Refrigerate the salad until chilled, at least 30 minutes.