Place a large Dutch oven or heavy-bottomed pot over medium heat. Add the diced bacon and cook until it is brown and crispy. Use a slotted spoon to remove the bacon bits and drain them on a paper towel, but leave about 3 tablespoons of the bacon drippings in the pot for flavor.

Add the chopped onion to the hot bacon grease. Sauté for about 5 minutes until the onion is translucent and soft. Stir in the minced garlic and cook for just 60 seconds until it becomes fragrant, being careful not to burn it.

Sprinkle the flour over the onions and garlic. Whisk constantly for 1 to 2 minutes to cook out the raw flour taste. Slowly pour in the chicken broth and milk while whisking vigorously to prevent lumps. Continue stirring until the liquid is smooth and begins to simmer.

Add the cubed potatoes to the pot. Bring the mixture to a gentle boil, then reduce the heat to low. Cover the pot and simmer for 15 to 20 minutes, or until the potatoes are fork-tender. If you prefer a smoother soup, use a potato masher to crush some of the potatoes directly in the pot.

Stir in the heavy cream, sour cream, and 1.5 cups of the shredded cheddar cheese. Stir until the cheese is completely melted and the soup is rich and velvety. Season with salt and pepper. If the soup is too thick, add a splash more milk until you reach your desired consistency.

Ladle the hot soup into deep bowls. Top each serving with the remaining shredded cheese, the crispy bacon bits, and a sprinkle of fresh chives. Serve immediately with a side of crusty bread for dipping.