Melt butter in a large saucepan over medium heat. Add onion and cook 2 minutes. Add garlic and cook 1 minute. Add potatoes and broth; bring to a boil. Reduce heat and simmer 12-14 minutes, or until potatoes are tender.
Remove from heat. Transfer mixture to a blender or food processor; pureé until smooth (you may need to do this in batches). Return mixture to saucepan. Alternately, blend the soup in the pot with an immersion blender. Stir in milk and heat over medium heat until hot (do not boil). Season to taste with salt and pepper. Stir in 1 cup cheddar cheese.
Ladle soup into four serving bowls. Evenly top each bowl with the remaining 1/2 cup cheddar, bacon, scallions and plain yogurt.