Prepare the potatoes. Wash, peel, and dice the russet potatoes into approximately ¾-inch cubes. Add them to a 6-quart slow cooker.
Add the vegetables. Add diced yellow onion and minced garlic to the crockpot with the potatoes.
Add the broth and seasonings. Pour chicken broth into the slow cooker. Add kosher salt, black pepper, and smoked paprika. Stir to combine.
Slow cook the potatoes. Cover and cook on low for 6-7 hours or high for 3-4 hours, until the potatoes are completely fork-tender.
Mash some of the potatoes. Use a potato masher to mash approximately one-third of the potatoes directly in the slow cooker. This will naturally thicken the broth while leaving plenty of potato chunks.
Add the creamy ingredients. Reduce the slow cooker to low. In a separate bowl, whisk softened cream cheese with a ladle of hot soup broth until smooth. Stir in the slightly warmed half-and-half, then add the mixture to the slow cooker.
Heat the soup. Cover and cook on low for another 15-20 minutes, or until the creamy mixture is heated through.
Add cheddar and sour cream. Turn off the slow cooker. Stir in 1½ cups of freshly shredded sharp cheddar cheese, a handful at a time, until melted. Add ½ cup sour cream and gently stir to combine.
Cook the bacon. While the soup finishes, cook bacon in a skillet over medium heat for 8-12 minutes, until crispy. Drain on paper towels and crumble.
Adjust the consistency. If the soup is too thick, stir in a splash of warm milk or chicken broth. Taste and adjust salt and pepper if needed.
Serve. Ladle the soup into bowls and top with crumbled bacon, the remaining ½ cup of cheddar cheese, sliced green onions, and additional sour cream if desired.