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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.
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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.
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Stir one cup of the cheddar cheese into the soup until melted and heated through.
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Ladle soup into four bowls; top with remaining 1/4 cup cheese.
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Garnish with crumbled bacon and chopped chives.