Scrub and dice the potatoes. These will be pulverized later so they don't need to be peeled and do not need to be super small. Do the same with the yellow onion. Place both in the Slow Cooker.
Add 4 Cups of Chicken broth. Add the Garlic and spices. Stir well and cover. Cook on low for 5-6 hours or high for 2 1/2 to 3 hours. If cooking on high, stir a least once.
Add the Cream cheese, slicing in thick chunks and cook for an additional 30 minutes. Then if you have an immersion blender, blenderize the potatoes and cream cheese. Add an additional 2 cups of Chicken broth and blend that in. If you don't have an immersion blender you can remove and use your blender, hand mixer, or a potato masher.
Add the frozen corn, carrots and ham, put on high for an additional 30 minutes. When that is done, add the cheddar cheese and blend well, taste test to see if you need any additional salt or pepper and add your paprika on top.