1) Heat the oil in a pan over medium-high heat. Once the oil is hot, sauté the onions until tender and very slightly starting to brown, about 10-12 minutes. Add carrots and continue to cook 5 minutes until carrot is soft (if using shredded carrots, skip this step and go straight to the slow cooker). Transfer cooked vegetables to the bowl of a 4-quart slow cooker.
2) Add the next seven ingredients, broth through pepper, to the slow cooker, and stir to combine. Cover and cook on low for 3 hours, or until vegetables are softened and rice is cooked.
3) About 30 minutes before serving the soup, mix in the half and half, broccoli, and cheese, cover, and cook on low for another 30 minutes. Add additional salt and pepper, to taste. Ladle soup into bowls, and garnish with toasted almonds and paprika, and enjoy.