1. In a large saucepan over medium heat, melt the butter. Add onions and sauté for 3-5 minutes until softened.
2. Stir in the garlic, cooking for about 30 seconds until fragrant.
3. Add the potatoes and broth, bringing to a boil. Reduce the heat and simmer for 12-14 minutes until the potatoes are tender.
4. Transfer 1 cup of the mixture to a blender or food processor and puree until smooth, then return it to the saucepan (use an immersion blender as an alternative).
5. Stir in the milk over low heat without boiling. Season with salt and pepper.
6. Gradually add 1 cup of shredded cheddar cheese, stirring until melted and incorporated.
7. Optionally, stir in sour cream and cook bacon for additional richness.
8. Ladle the soup into bowls, topping with the remaining cheese. Garnish with bacon, chives, or extra sour cream as desired.