Cook 4 halved bacon slices in a single layer in a Dutch oven or large pot over medium heat, flipping halfway through, until browned and crisp, 8 to 10 minutes total. Using tongs, transfer to a paper towel-lined plate.

Add 1 finely chopped medium yellow onion to the bacon fat. Cook, stirring occasionally, until softened, about 5 minutes. Increase the heat to high, add 1 cup low-sodium chicken broth, and scrape up any browned bits from the bottom of the pot. Stir in 4 cups whole milk, 1 ¾ teaspoons kosher salt, and ¼ teaspoon black pepper. Bring to a boil.

Stir in 2 pounds peeled and chopped russet potatoes and bring to a simmer. Simmer, stirring occasionally, until the potatoes are tender, 8 to 10 minutes. Meanwhile, crumble the bacon with your hands into small pieces.

Turn off the heat. For a smooth soup, purée the soup in batches in a stand blender until smooth, then return to the pot (or blend directly in the pot with an immersion blender). For a chunky smooth, only blend half the soup or smash the potatoes with a potato masher until the soup is the desired consistency.

Return the soup to low heat. Stir in 4 ounces shredded sharp cheddar cheese until melted. Turn off the heat. Stir in ¼ cup sour cream. Taste and season with more kosher salt and black pepper as needed. Serve garnished with the crumbled bacon, finely chopped fresh chives, and more shredded sharp cheddar cheese as desired.