Heat a large soup pot over medium heat. Add in sausage and cook until browned, stirring occasionally. Use a slotted spoon to remove cooked sausage and set aside.
Return pot to medium-high heat. Add in onion and sauté 7 minutes, until soft and translucent. Add in butter and garlic and stir until butter is melted.
Slowly pour in chicken broth and milk. Add in potatoes and bring to a simmer. Reduce the heat to medium-low and continue simmering until potatoes are soft and tender, about 15 minutes.
Once potatoes are tender, gently mash the potatoes, but not too aggressively so that you can still have some texture and chunks of potatoes. Stir in sour cream and add in the cooked sausage. Season with salt and pepper to taste.
Serve hot topped with chives, cheese, and an additional dollop of sour cream.