Sauté the aromatics. In a large pot or Dutch oven, melt the butter over medium heat.
Add the onion and celery. Cook for 5–6 minutes, stirring occasionally, until softened and translucent. Stir in the garlic and cook for 30 seconds, just until fragrant.
Add the hashbrowns. Pour in the frozen shredded hashbrowns.
Stir to coat with the aromatics and butter. Cook for 2–3 minutes to take the chill off.
Pour in the broth. Add the chicken or vegetable broth, salt, pepper, onion powder, and smoked paprika. Stir well, then bring to a gentle simmer.
Simmer and thicken. Cover partially and simmer for 15–20 minutes, stirring occasionally.
The potatoes will soften and release starch, naturally thickening the soup.
Add dairy. Lower the heat to medium-low. Stir in the milk or half-and-half and the sour cream. Warm through slowly.
Do not boil after adding dairy, or it may split.
Finish with cheese. Stir in the shredded cheddar until fully melted and smooth. Taste and adjust seasoning with more salt and pepper as needed.
Serve. Ladle into bowls and top with more cheddar, bacon, and chives. Serve with crusty bread or a simple salad.