Sauté aromatics & build roux: Melt 4 tablespoons of butter in a large Dutch oven or heavy soup pot over medium heat. Add diced onion and cook for 4 to 5 minutes until soft and translucent. Add minced garlic and cook for 1 minute until fragrant. Sprinkle flour over the onions and cook, stirring continuously for 1 to 2 minutes to cook off raw flour flavor.

Simmer potatoes: Slowly whisk in the chicken broth, whole milk, and heavy cream, smoothing out any lumps. Add the cubed russet potatoes, salt, and black pepper. Bring to a gentle boil, then reduce heat to medium-low, cover partially with the lid, and simmer for 12 to 15 minutes until potatoes are fork-tender.

Mash to desired texture: Using a potato masher, press down into the pot several times to crush about half of the potatoes. This naturally thickens the soup broth while leaving plenty of hearty, tender potato chunks throughout.

Melt cheese & stir sour cream: Reduce heat to low. Whisk in the sour cream until smooth and incorporated. Gradually stir in 2 cups of freshly shredded sharp cheddar cheese one handful at a time until completely melted and velvety smooth. Remove from heat (do not let boil after adding cheese).

Garnish & serve: Taste and adjust salt and pepper if needed. Ladle steaming hot soup into ceramic bowls and top generously with additional shredded cheddar, a dollop of sour cream, finely chopped fresh chives, and cracked black pepper. Serve warm with crusty bread!