Peel and cube the potatoes, chop the onion and garlic, and measure out the butter, chicken broth, heavy cream, and seasonings.
In a large pot, melt the butter over medium heat and sauté the chopped onion and garlic until softened and fragrant, about 3-5 minutes.
Add the cubed potatoes to the pot, then pour in the chicken broth, ensuring the potatoes are covered. Bring the mixture to a simmer and cook until the potatoes are tender, about 15-20 minutes.
Once the potatoes are tender, use a potato masher or an immersion blender to mash the potatoes to your desired texture, leaving some chunks for a rustic feel.
Stir in the heavy cream, sour cream, salt, and pepper. Let the soup simmer for an additional 5 minutes to thicken and meld the flavors.
Once the soup is creamy and heated through, serve it topped with shredded cheddar cheese and chives. Enjoy the rich, comforting bowl of potato soup!