In a large sauce pan, whisk together the non-dairy milk and carrot juice.
Heat the sauce pan on medium high and then add the brown sugar, cane sugar and salt. Whisk to combine. Bring to a simmer and continue to whisk until the sugars have dissolved.
Pour in the rice, whisk, then reduce the heat to medium low and then cover the pan.
Simmer the rice, making sure it is just at a small bubble so the pan doesn't overflow, for 60 to 70 minutes or until the rice has thickened. Stir the rice every 10 minutes or so. Then re-cover the pan.
Once the rice has thickened up, and most of the liquid has been absorbed, just keep in mind that it will still be a little liquidy and it thickens as it cools, turn off the heat.
Then pour in the vanilla and all the spices, stir them into the rice pudding.
Let it cool to room temperature on the stove top. Then put in the fridge and cool completely. At least 4 to 6 hours, but I like to chill over night.
When the rice pudding has cooled completely and is very thick, stir in the walnuts and raisins. Then serve! Keep in the fridge until serving.