Sauté the leeks – Melt butter in a large pot over medium heat. Add sliced leeks, season with salt and pepper, and cook until soft and fragrant (about 5 minutes).
Make a roux – Stir in cornstarch and cook for 1 minute to remove the raw taste.
Simmer the potatoes – Pour in chicken broth, add diced potatoes, and bring to a boil. Reduce heat and simmer until potatoes are tender (about 15 minutes).
Blend until smooth – Use an immersion blender or transfer to a blender to purée until creamy.
Add the cream – Stir in heavy cream, adjust seasoning, and let it warm through without boiling.
Serve and enjoy – Ladle into bowls, garnish with fresh herbs or croutons, and serve warm.