In a heavy bottomed pot, heat milk over medium heat until it comes to a low boil, stirring often to prevent the milk from burning.
Add grated carrots and stir. Once the milk returns to a boil, reduce heat to medium-low and cook until the carrots have softened considerably, about 20 to 30 minutes. Be sure to stir often.
In a small bowl, whisk together sugar and ground cardamom. Add sugar mixture to carrots and mix well. Add ground rice and condensed milk and mix until thoroughly combined. Cook, while stirring often to prevent burning, until significantly reduced and thickened, about 30 minutes.
Garnish with additional sliced nuts, if desired.
Refrigerate until ready to serve.