This fantastic soup is a perfect combination of early spring vegetables - the last of the sweet potatoes meet the first carrots. Add in some sharp cheddar and you have a soup everyone in the family will love!
In a large dutch oven or pot, heat butter or oil over medium heat, and then add onions, carrots, and sweet potatoes. Let sauté about 5 minutes.
Add the apple juice and cook until it is mostly absorbed. Add the broth and bring to a boil. Reduce heat, and let simmer, covered, until vegetables are very soft (about 20-30 minutes, depending on how small you've diced them).
With an immersion blender, blend soup until smooth (or carefully transfer it to a traditional blender and puree in batches, before returning it to the pot).
Add shredded cheese, stirring occasionally, until fully melted and combined. Stir in half-and-half. Add salt and pepper to taste before serving.