Cook the beef bacon in a large pot or Dutch oven over medium heat until crispy. Remove the beef bits with a slotted spoon and set aside. Drain all but 1 tablespoon of the drippings.
Add the unsalted butter to the pot and melt over medium heat. Whisk in the all-purpose flour and cook for 1 minute to form a roux.
Gradually pour in the whole milk and chicken broth, whisking constantly until the mixture is smooth and begins to thicken.
Stir in the diced russet potatoes, salt, and black pepper. Bring the soup to a gentle simmer, cover, and cook for 15 minutes, or until the potatoes are fork-tender.
Remove the pot from the heat. Stir in the sour cream and 1 cup of the shredded sharp cheddar cheese until melted and smooth.
Ladle the hot soup into bowls. Top with the remaining 1 cup of cheddar cheese, crispy beef bits, and fresh chopped chives before serving.