Melt butter in a large saucepan over medium heat.
Add onion; sauté 3 minutes.
Add garlic; sauté 2 minutes.
Add potatoes and broth; bring to a boil.
Reduce heat; simmer 12 to 14 minutes or until vegetables are tender.
Transfer 1 cup of the mixture to a blender or food processor; pureé until smooth.
Return mixture to saucepan.
Stir in milk; heat over medium heat until hot (do not boil).
Season to taste with salt and pepper.
Stir 1 cup of the cheddar cheese into the soup until melted and heated through.
Ladle soup into four bowls; top with remaining ¼ cup cheese.
Garnish with crumbled bacon and chopped chives.