First, preheat your oven to 225 degrees.
Line a rimmed baking sheet with parchment paper and coat it lightly with nonstick spray.
Using a vegetable peeler, shave off 15 to 20 long strips of carrot.
In a medium saucepan, combine 1 cup of water and 1 cup of sugar. Bring this mixture to a boil, stirring until the sugar dissolves completely.
Once the syrup is boiling, add in the carrot strips. Reduce the heat to medium-low and let them simmer for 15 minutes.
After simmering, drain the carrots well and let them cool for about 5 minutes.
Arrange the carrot strips in a single layer on the prepared baking sheet.
Now, bake those strips in the preheated oven until they begin to look translucent, which should take about 30 minutes.
As soon as they’re cool enough to handle but still warm, wrap each carrot strip around the handle of a wooden spoon to form curls.
Let the curls sit at room temperature until they’re completely dry, about 30 minutes.
