In a large heavy-bottomed pot or Dutch oven over medium heat, cook the bacon pieces until crispy, about 6–8 minutes. Using a slotted spoon, transfer the bacon to a paper towel-lined plate and set aside, leaving the rendered bacon fat in the pot.

Add the diced onion to the pot with the bacon fat over medium heat. Cook, stirring occasionally, until softened and translucent, about 4–5 minutes. Add the minced garlic and cook for 1 minute more until fragrant.

Sprinkle the flour over the onion mixture and stir to coat. Cook for 1–2 minutes, stirring constantly, to cook out the raw flour taste.

Slowly pour in the chicken broth while whisking to prevent lumps, scraping up any browned bits from the bottom of the pot. Add the milk, diced potatoes, salt, pepper, and smoked paprika. Stir to combine.

Bring the soup to a boil over medium-high heat, then reduce heat to medium-low and simmer uncovered for 15–18 minutes, stirring occasionally, until the potatoes are completely tender and easily pierced with a fork.

Using a potato masher or the back of a large wooden spoon, mash roughly one-third of the potatoes directly in the pot. Stir well — this will naturally thicken the soup while leaving hearty chunks throughout.

Reduce the heat to very low. Stir in the sour cream and 1.5 cups of shredded cheddar cheese until fully melted and incorporated. Taste and adjust seasoning with additional salt and pepper as needed.

Ladle the soup into bowls and top each serving with reserved crispy bacon crumbles, additional shredded cheddar, a dollop of sour cream, and a generous scatter of fresh chives. Serve immediately.