Shred the carrots on the largest holes of a box grater, or using a food processor. Combine shredded carrot with milk, half-and-half, cardamom and cinnamon in a large, heavy-bottomed pot (at least 6 qts). Bring to a boil, then reduce to a simmer. Cook, stirring occasionally, until all the milk has cooked off and the mixture is nearly dry, 40-60 minutes.