Start by peeling and dicing the russet potatoes into uniform cubes. Chop the onion, carrots, and celery; mince the garlic.

In a large pot, heat the butter or olive oil over medium heat. Add the onion and garlic, cooking until the onions are translucent, about 4-5 minutes.

Add the diced potatoes, carrots, and celery to the pot, stirring to combine. Pour in the broth, bring to a boil, then reduce heat to low and simmer for about 40 minutes.

After the vegetables are tender, mash about a quarter of the potato cubes in the pot to thicken the soup.

Gradually stir in the whole milk and heavy cream, then add the shredded cheddar cheese, stirring until melted and smooth.

Season with salt and pepper to taste, then ladle into bowls and garnish with chives and paprika.