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Melt butter in a large pot over medium heat. Add sliced leeks and cook 5-7 minutes until softened.
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Add cubed potatoes and chicken broth. Bring to a boil, then reduce to a simmer. Cook 15-20 minutes until potatoes are very tender.
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Use an immersion blender to blend until mostly smooth (leave some chunks for texture if you like).
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Stir in heavy cream and thyme. Season generously with salt and pepper. Heat through on low for 5 minutes.
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Ladle into bowls and garnish with chopped chives. Serve with crusty bread.